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> library(robustbase)
>
> source(system.file("xtraR/test_MCD.R", package = "robustbase"))#-> doMCDdata
> ## ../inst/xtraR/test_MCD.R
> ## instead of relying on system.file("test-tools-1.R", package="Matrix"):
> source(system.file("xtraR/test-tools.R", package = "robustbase")) # showProc.time(), relErr()
> showProc.time()
Time (user system elapsed): 0 0 0
>
> ## -- now do it:
> options(digits = 5)
> set.seed(101) # <<-- sub-sampling algorithm now based on R's RNG and seed
> doMCDdata()
Call: doMCDdata()
Data Set n p h(alf) LOG(obj)
=============================================
bushfire 38 5 22 18.135810
Best subsample:
[1] 1 2 3 4 5 6 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Outliers: 16 :
[1] 7 8 9 10 11 12 29 30 31 32 33 34 35 36 37 38
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=22); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 18.1
Robust Estimate of Location:
V1 V2 V3 V4 V5
105 147 274 218 279
Robust Estimate of Covariance:
V1 V2 V3 V4 V5
V1 346 268 -1692 -381 -311
V2 268 236 -1125 -230 -194
V3 -1692 -1125 9993 2455 1951
V4 -381 -230 2455 647 505
V5 -311 -194 1951 505 398
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
heart 12 2 7 5.678742
Best subsample:
[1] 1 3 4 5 7 9 11
Outliers: 0
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=7); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 5.68
Robust Estimate of Location:
height weight
38.3 33.1
Robust Estimate of Covariance:
height weight
height 135 259
weight 259 564
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
starsCYG 47 2 25 -8.031215
Best subsample:
[1] 1 2 4 6 8 10 12 13 16 24 25 26 28 32 33 37 38 39 40 41 42 43 44 45 46
Outliers: 7 :
[1] 7 9 11 14 20 30 34
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=25); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): -8.03
Robust Estimate of Location:
log.Te log.light
4.41 4.95
Robust Estimate of Covariance:
log.Te log.light
log.Te 0.0132 0.0394
log.light 0.0394 0.2743
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
stackloss 21 3 12 5.472581
Best subsample:
[1] 4 5 6 7 8 9 10 11 12 13 14 20
Outliers: 9 :
[1] 1 2 3 15 16 17 18 19 21
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=12); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 5.47
Robust Estimate of Location:
Air.Flow Water.Temp Acid.Conc.
59.5 20.8 87.3
Robust Estimate of Covariance:
Air.Flow Water.Temp Acid.Conc.
Air.Flow 6.29 5.85 5.74
Water.Temp 5.85 9.23 6.14
Acid.Conc. 5.74 6.14 23.25
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
phosphor 18 2 10 6.878847
Best subsample:
[1] 3 5 8 9 11 12 13 14 15 17
Outliers: 3 :
[1] 1 6 10
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=10); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 6.88
Robust Estimate of Location:
inorg organic
13.4 38.8
Robust Estimate of Covariance:
inorg organic
inorg 129 130
organic 130 182
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
coleman 20 5 13 1.286808
Best subsample:
[1] 2 3 4 5 7 8 12 13 14 16 17 19 20
Outliers: 7 :
[1] 1 6 9 10 11 15 18
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=13); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 1.29
Robust Estimate of Location:
salaryP fatherWc sstatus teacherSc motherLev
2.76 48.38 6.12 25.00 6.40
Robust Estimate of Covariance:
salaryP fatherWc sstatus teacherSc motherLev
salaryP 0.253 1.79 -0.266 0.151 0.075
fatherWc 1.786 1303.38 330.496 12.604 34.503
sstatus -0.266 330.50 119.888 3.833 10.131
teacherSc 0.151 12.60 3.833 0.785 0.555
motherLev 0.075 34.50 10.131 0.555 1.043
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
salinity 28 3 16 1.326364
Best subsample:
[1] 1 2 6 7 8 12 13 14 18 20 21 22 25 26 27 28
Outliers: 4 :
[1] 5 16 23 24
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=16); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 1.33
Robust Estimate of Location:
X1 X2 X3
10.08 2.78 22.78
Robust Estimate of Covariance:
X1 X2 X3
X1 10.44 1.01 -3.19
X2 1.01 3.83 -1.44
X3 -3.19 -1.44 2.39
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
wood 20 5 13 -36.270094
Best subsample:
[1] 1 2 3 5 9 10 12 13 14 15 17 18 20
Outliers: 7 :
[1] 4 6 7 8 11 16 19
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=13); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): -36.3
Robust Estimate of Location:
x1 x2 x3 x4 x5
0.587 0.122 0.531 0.538 0.892
Robust Estimate of Covariance:
x1 x2 x3 x4 x5
x1 0.010025 1.88e-03 0.003153 -0.000586 -1.63e-03
x2 0.001881 4.85e-04 0.001269 -0.000052 2.36e-05
x3 0.003153 1.27e-03 0.006632 -0.000871 3.52e-04
x4 -0.000586 -5.20e-05 -0.000871 0.002846 1.83e-03
x5 -0.001630 2.36e-05 0.000352 0.001828 2.77e-03
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
hbk 75 3 39 -1.047858
Best subsample:
[1] 15 16 17 18 19 20 21 22 23 24 26 27 31 32 33 35 36 37 38 40 43 49 50 51 54
[26] 55 56 58 59 61 63 64 66 67 70 71 72 73 74
Outliers: 14 :
[1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=39); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): -1.05
Robust Estimate of Location:
X1 X2 X3
1.54 1.78 1.69
Robust Estimate of Covariance:
X1 X2 X3
X1 1.227 0.055 0.127
X2 0.055 1.249 0.153
X3 0.127 0.153 1.160
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
Animals 28 2 15 14.555543
Best subsample:
[1] 1 3 4 5 10 11 17 18 19 20 21 22 23 26 27
Outliers: 14 :
[1] 2 6 7 8 9 12 13 14 15 16 23 24 25 28
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=15); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 14.6
Robust Estimate of Location:
body brain
18.7 64.9
Robust Estimate of Covariance:
body brain
body 929 1576
brain 1576 5646
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
milk 86 8 47 -28.837261
Best subsample:
[1] 5 7 8 9 10 21 22 24 30 31 32 33 34 35 38 39 45 46 51 53 54 55 56 57 58
[26] 59 60 61 62 63 64 65 66 67 68 69 71 72 76 78 79 80 81 82 83 84 86
Outliers: 20 :
[1] 1 2 3 11 12 13 14 15 16 17 18 20 27 41 44 47 70 74 75 77
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=47); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): -28.8
Robust Estimate of Location:
X1 X2 X3 X4 X5 X6 X7 X8
1.03 35.87 33.09 26.15 25.13 25.06 123.14 14.39
Robust Estimate of Covariance:
X1 X2 X3 X4 X5 X6 X7
X1 3.86e-07 0.000115 0.000135 0.000132 0.000118 0.000101 0.000538
X2 1.15e-04 1.901695 0.321524 0.228041 0.164447 0.261330 1.804532
X3 1.35e-04 0.321524 1.189750 0.869795 0.851445 0.857952 0.777883
X4 1.32e-04 0.228041 0.869795 0.684723 0.651039 0.652613 0.603585
X5 1.18e-04 0.164447 0.851445 0.651039 0.680275 0.655047 0.608406
X6 1.01e-04 0.261330 0.857952 0.652613 0.655047 0.680328 0.601059
X7 5.38e-04 1.804532 0.777883 0.603585 0.608406 0.601059 4.022100
X8 1.29e-05 0.238712 0.201708 0.132675 0.115217 0.125472 0.389816
X8
X1 1.29e-05
X2 2.39e-01
X3 2.02e-01
X4 1.33e-01
X5 1.15e-01
X6 1.25e-01
X7 3.90e-01
X8 1.54e-01
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
lactic 20 2 11 0.359580
Best subsample:
[1] 1 2 3 4 5 7 8 9 10 11 12
Outliers: 4 :
[1] 17 18 19 20
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=11); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 0.36
Robust Estimate of Location:
X Y
3.86 5.01
Robust Estimate of Covariance:
X Y
X 10.6 14.6
Y 14.6 21.3
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
pension 18 2 10 16.675508
Best subsample:
[1] 1 2 3 4 5 6 8 9 11 12
Outliers: 5 :
[1] 14 15 16 17 18
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=10); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 16.7
Robust Estimate of Location:
Income Reserves
52.3 560.9
Robust Estimate of Covariance:
Income Reserves
Income 1420 11932
Reserves 11932 208643
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
pilot 20 2 11 6.487287
Best subsample:
[1] 2 3 6 7 9 12 15 16 17 18 20
Outliers: 0
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=11); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 6.49
Robust Estimate of Location:
X Y
101.1 67.7
Robust Estimate of Covariance:
X Y
X 3344 1070
Y 1070 343
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
vaso 39 2 21 -3.972244
Best subsample:
[1] 3 4 8 14 18 19 20 21 22 23 24 25 26 27 28 33 34 35 37 38 39
Outliers: 4 :
[1] 1 2 17 31
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=21); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): -3.97
Robust Estimate of Location:
Volume Rate
1.16 1.72
Robust Estimate of Covariance:
Volume Rate
Volume 0.313 -0.167
Rate -0.167 0.728
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
wagnerGrowth 63 6 35 6.569262
Best subsample:
[1] 2 3 4 5 6 7 9 10 11 12 14 16 17 18 20 23 25 27 31 32 35 36 38 41 44
[26] 48 52 53 54 55 56 57 58 60 62
Outliers: 17 :
[1] 1 8 15 21 22 24 26 28 29 33 39 42 43 46 50 61 63
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=35); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 6.57
Robust Estimate of Location:
Region PA GPA HS GHS y
11.318 34.050 -2.049 2.498 0.289 6.650
Robust Estimate of Covariance:
Region PA GPA HS GHS y
Region 32.797 14.685 -1.650 -1.0301 -0.2907 -10.601
PA 14.685 25.961 -6.038 -1.5554 0.1318 -25.877
GPA -1.650 -6.038 5.352 0.3838 -0.1690 4.583
HS -1.030 -1.555 0.384 0.9156 -0.0486 3.194
GHS -0.291 0.132 -0.169 -0.0486 0.1205 -0.209
y -10.601 -25.877 4.583 3.1936 -0.2085 70.718
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
fish 158 6 82 8.878062
Best subsample:
[1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
[20] 20 21 22 23 24 25 26 27 28 30 31 32 35 36 37 42 43 44 45
[39] 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 107 109 110 111
[58] 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130
[77] 131 134 135 136 137 139
Outliers: 69 :
[1] 29 38 39 40 41 61 62 63 64 65 66 67 68 69 70 71 72 73 74
[20] 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93
[39] 94 95 96 97 98 99 100 101 102 103 104 133 140 141 142 143 144 145 146
[58] 147 148 149 150 151 152 153 154 155 156 157 158
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=82); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 8.88
Robust Estimate of Location:
Weight Length1 Length2 Length3 Height Width
331.9 24.4 26.6 29.7 31.2 14.7
Robust Estimate of Covariance:
Weight Length1 Length2 Length3 Height Width
Weight 75099.7 1549.5 1699.2 2119.44 1638.37 -69.924
Length1 1549.5 35.3 38.4 47.11 32.40 -1.697
Length2 1699.2 38.4 41.9 51.43 35.78 -1.797
Length3 2119.4 47.1 51.4 64.10 47.40 -2.549
Height 1638.4 32.4 35.8 47.40 48.97 -2.586
Width -69.9 -1.7 -1.8 -2.55 -2.59 0.833
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
pottery 27 6 17 -10.586933
Best subsample:
[1] 1 2 4 5 6 9 10 11 13 14 15 19 20 21 22 26 27
Outliers: 9 :
[1] 3 8 12 16 17 18 23 24 25
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=17); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): -10.6
Robust Estimate of Location:
SI AL FE MG CA TI
54.983 15.206 9.700 3.817 5.211 0.859
Robust Estimate of Covariance:
SI AL FE MG CA TI
SI 20.5823 2.2874 -0.0204 2.1265 -1.8023 0.08821
AL 2.2874 4.0361 -0.6302 -2.4997 0.2084 -0.02038
FE -0.0204 -0.6302 0.2780 0.5338 -0.3512 0.01427
MG 2.1265 -2.4997 0.5338 2.7956 -0.1579 0.02847
CA -1.8023 0.2084 -0.3512 -0.1579 1.2324 -0.03465
TI 0.0882 -0.0204 0.0143 0.0285 -0.0347 0.00175
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
rice 105 6 56 -14.438945
Best subsample:
[1] 2 4 6 8 10 12 15 17 18 21 24 27 29 30 31 32 33 34 36
[20] 37 38 41 44 45 47 51 52 53 55 59 60 61 65 67 70 72 76 78
[39] 79 80 81 82 83 84 85 86 90 92 93 94 95 97 98 99 102 105
Outliers: 11 :
[1] 9 28 40 42 49 58 62 64 71 75 77
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=56); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): -14.4
Robust Estimate of Location:
Favor Appearance Taste Stickiness
-0.2844 0.0786 -0.1453 0.0378
Toughness Overall_evaluation
0.0833 -0.2363
Robust Estimate of Covariance:
Favor Appearance Taste Stickiness Toughness
Favor 0.453 0.373 0.449 0.425 -0.198
Appearance 0.373 0.598 0.576 0.568 -0.318
Taste 0.449 0.576 0.723 0.695 -0.379
Stickiness 0.425 0.568 0.695 0.834 -0.470
Toughness -0.198 -0.318 -0.379 -0.470 0.439
Overall_evaluation 0.534 0.661 0.815 0.843 -0.465
Overall_evaluation
Favor 0.534
Appearance 0.661
Taste 0.815
Stickiness 0.843
Toughness -0.465
Overall_evaluation 0.986
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
un86 73 7 40 17.017767
Best subsample:
[1] 1 9 10 12 14 16 17 18 20 23 24 26 27 31 33 37 39 41 42 45 47 48 49 50 51
[26] 52 55 56 57 60 61 62 63 64 65 67 70 71 72 73
Outliers: 29 :
[1] 3 4 5 6 7 8 11 13 15 19 21 22 28 29 30 35 36 38 40 43 44 46 53 54 58
[26] 59 66 68 69
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=40); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 17
Robust Estimate of Location:
POP MOR CAR DR GNP DEN TB
20.364 69.750 6.463 0.859 1.133 59.998 0.439
Robust Estimate of Covariance:
POP MOR CAR DR GNP DEN TB
POP 575.827 243.29 -12.910 -2.4098 -3.0456 160.82 0.4208
MOR 243.291 2376.56 -282.081 -33.9548 -33.9168 -718.68 -1.0522
CAR -12.910 -282.08 56.808 5.6651 6.4636 86.27 0.2616
DR -2.410 -33.95 5.665 0.9009 0.5568 18.60 0.0154
GNP -3.046 -33.92 6.464 0.5568 1.3929 10.67 0.0067
DEN 160.825 -718.68 86.269 18.6034 10.6747 2512.64 -1.1705
TB 0.421 -1.05 0.262 0.0154 0.0067 -1.17 0.0181
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
wages 36 9 23 25.658041
Best subsample:
[1] 1 2 3 6 7 8 10 11 12 14 15 17 20 21 22 23 25 26 27 33 34 35 36
Outliers: 13 :
[1] 4 5 9 13 16 18 19 24 28 29 30 31 32
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=23); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 25.7
Robust Estimate of Location:
HRS RATE ERSP ERNO NEIN ASSET AGE DEP
2140.17 2.85 1133.30 307.48 343.26 6539.43 39.57 2.44
SCHOOL
10.07
Robust Estimate of Covariance:
HRS RATE ERSP ERNO NEIN ASSET
HRS 4433.91 19.7358 -3585.03 -990.563 8227.4 184546
RATE 19.74 0.2393 8.06 1.048 59.2 1373
ERSP -3585.03 8.0565 12399.96 995.108 -4363.3 -78026
ERNO -990.56 1.0481 995.11 2190.581 -426.0 -9925
NEIN 8227.37 59.1712 -4363.27 -425.985 19585.3 441574
ASSET 184546.39 1373.0630 -78025.61 -9925.182 441574.2 10017473
AGE -46.58 -0.2052 18.34 19.517 -83.0 -1898
DEP -6.57 -0.0985 -2.85 0.499 -20.6 -471
SCHOOL 59.89 0.5677 7.54 -4.821 153.0 3541
AGE DEP SCHOOL
HRS -4.66e+01 -6.5659 59.885
RATE -2.05e-01 -0.0985 0.568
ERSP 1.83e+01 -2.8522 7.540
ERNO 1.95e+01 0.4986 -4.821
NEIN -8.30e+01 -20.6329 153.022
ASSET -1.90e+03 -471.1344 3540.557
AGE 7.72e-01 0.0412 -0.684
DEP 4.12e-02 0.0873 -0.240
SCHOOL -6.84e-01 -0.2402 1.453
--------------------------------------------------------
========================================================
> doMCDdata(method="DetMCD"); warnings()
Call: doMCDdata(method = "DetMCD")
Data Set n p h(alf) LOG(obj)
=============================================
bushfire 38 5 22 18.135810
Best subsample:
[1] 1 2 3 4 5 6 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Outliers: 16 :
[1] 7 8 9 10 11 12 29 30 31 32 33 34 35 36 37 38
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=22)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 2, 3, 6; C-step iterations: 2, 3, 3, 2, 2, 3
Log(Det.): 18.1
Robust Estimate of Location:
V1 V2 V3 V4 V5
105 147 274 218 279
Robust Estimate of Covariance:
V1 V2 V3 V4 V5
V1 346 268 -1692 -381 -311
V2 268 236 -1125 -230 -194
V3 -1692 -1125 9993 2455 1951
V4 -381 -230 2455 647 505
V5 -311 -194 1951 505 398
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
heart 12 2 7 5.678742
Best subsample:
[1] 1 3 4 5 7 9 11
Outliers: 0
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=7)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 2, 3, 4, 6; C-step iterations: 2, 2, 2, 2, 2, 2
Log(Det.): 5.68
Robust Estimate of Location:
height weight
38.3 33.1
Robust Estimate of Covariance:
height weight
height 135 259
weight 259 564
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
starsCYG 47 2 25 -8.028718
Best subsample:
[1] 1 6 10 12 13 16 23 24 25 26 28 31 32 33 37 38 39 40 41 42 43 44 45 46 47
Outliers: 7 :
[1] 7 9 11 14 20 30 34
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=25)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 5; C-step iterations: 4, 4, 4, 4, 4, 4
Log(Det.): -8.03
Robust Estimate of Location:
log.Te log.light
4.41 4.95
Robust Estimate of Covariance:
log.Te log.light
log.Te 0.0132 0.0394
log.light 0.0394 0.2743
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
stackloss 21 3 12 6.577286
Best subsample:
[1] 4 5 6 7 8 9 11 13 16 18 19 20
Outliers: 2 :
[1] 1 2
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=12)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 6; C-step iterations: 3, 3, 3, 3, 2, 2
Log(Det.): 6.58
Robust Estimate of Location:
Air.Flow Water.Temp Acid.Conc.
58.4 20.5 86.1
Robust Estimate of Covariance:
Air.Flow Water.Temp Acid.Conc.
Air.Flow 56.3 13.33 26.68
Water.Temp 13.3 8.28 6.98
Acid.Conc. 26.7 6.98 37.97
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
phosphor 18 2 10 7.732906
Best subsample:
[1] 2 4 5 7 8 9 11 12 14 16
Outliers: 1 :
[1] 6
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=10)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 4; C-step iterations: 3, 3, 3, 3, 3, 3
Log(Det.): 7.73
Robust Estimate of Location:
inorg organic
12.5 40.8
Robust Estimate of Covariance:
inorg organic
inorg 124 101
organic 101 197
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
coleman 20 5 13 2.149184
Best subsample:
[1] 3 4 5 7 8 12 13 14 16 17 18 19 20
Outliers: 2 :
[1] 6 10
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=13)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 5; C-step iterations: 2, 2, 2, 2, 2, 3
Log(Det.): 2.15
Robust Estimate of Location:
salaryP fatherWc sstatus teacherSc motherLev
2.76 41.08 2.76 25.01 6.27
Robust Estimate of Covariance:
salaryP fatherWc sstatus teacherSc motherLev
salaryP 0.391 2.96 2.15 0.447 0.110
fatherWc 2.956 1358.64 442.72 12.235 32.842
sstatus 2.146 442.72 205.59 6.464 11.382
teacherSc 0.447 12.23 6.46 1.179 0.510
motherLev 0.110 32.84 11.38 0.510 0.919
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
salinity 28 3 16 1.940763
Best subsample:
[1] 1 8 10 12 13 14 15 17 18 20 21 22 25 26 27 28
Outliers: 2 :
[1] 5 16
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=16)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 4, 5; C-step iterations: 2, 2, 2, 3, 2, 2
Log(Det.): 1.94
Robust Estimate of Location:
X1 X2 X3
10.50 2.58 23.12
Robust Estimate of Covariance:
X1 X2 X3
X1 10.90243 -0.00457 -1.46
X2 -0.00457 3.85051 -1.95
X3 -1.46156 -1.94604 3.21
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
wood 20 5 13 -35.240819
Best subsample:
[1] 1 2 3 5 9 11 12 13 14 15 17 18 20
Outliers: 4 :
[1] 4 6 8 19
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=13)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 2; C-step iterations: 2, 2, 2, 2, 2, 2
Log(Det.): -35.2
Robust Estimate of Location:
x1 x2 x3 x4 x5
0.582 0.125 0.530 0.534 0.888
Robust Estimate of Covariance:
x1 x2 x3 x4 x5
x1 0.010502 0.001810 2.08e-03 -0.000641 -9.61e-04
x2 0.001810 0.000555 8.76e-04 -0.000203 -4.70e-05
x3 0.002081 0.000876 5.60e-03 -0.001106 -1.26e-05
x4 -0.000641 -0.000203 -1.11e-03 0.004266 2.60e-03
x5 -0.000961 -0.000047 -1.26e-05 0.002602 2.95e-03
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
hbk 75 3 39 -1.045501
Best subsample:
[1] 15 17 18 19 20 21 22 23 24 26 27 28 29 32 33 35 36 38 40 41 43 48 49 50 51
[26] 54 55 56 58 59 63 64 66 67 70 71 72 73 74
Outliers: 14 :
[1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=39)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 2, 3, 4, 6; C-step iterations: 5, 5, 5, 5, 4, 5
Log(Det.): -1.05
Robust Estimate of Location:
X1 X2 X3
1.54 1.78 1.69
Robust Estimate of Covariance:
X1 X2 X3
X1 1.227 0.055 0.127
X2 0.055 1.249 0.153
X3 0.127 0.153 1.160
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
Animals 28 2 15 14.555543
Best subsample:
[1] 1 3 4 5 10 11 17 18 19 20 21 22 23 26 27
Outliers: 14 :
[1] 2 6 7 8 9 12 13 14 15 16 23 24 25 28
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=15)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 2, 3, 4, 5, 6; C-step iterations: 2, 2, 2, 2, 2, 2
Log(Det.): 14.6
Robust Estimate of Location:
body brain
18.7 64.9
Robust Estimate of Covariance:
body brain
body 929 1576
brain 1576 5646
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
milk 86 8 47 -28.844954
Best subsample:
[1] 5 8 9 10 21 22 23 24 26 30 31 32 33 34 35 36 37 38 39 46 51 53 54 55 56
[26] 57 58 59 60 61 62 63 64 65 66 67 68 69 71 72 76 78 79 81 83 84 86
Outliers: 20 :
[1] 1 2 3 11 12 13 14 15 16 17 18 20 27 41 44 47 70 74 75 77
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=47)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 5; C-step iterations: 3, 3, 4, 3, 3, 4
Log(Det.): -28.8
Robust Estimate of Location:
X1 X2 X3 X4 X5 X6 X7 X8
1.03 35.90 33.10 26.16 25.13 25.07 123.13 14.39
Robust Estimate of Covariance:
X1 X2 X3 X4 X5 X6 X7
X1 4.62e-07 8.16e-05 0.000162 0.000159 0.000141 0.000132 0.000604
X2 8.16e-05 1.73e+00 0.199526 0.156489 0.081711 0.201994 1.499551
X3 1.62e-04 2.00e-01 1.148093 0.849962 0.824682 0.847271 0.650728
X4 1.59e-04 1.56e-01 0.849962 0.676140 0.638434 0.649539 0.547968
X5 1.41e-04 8.17e-02 0.824682 0.638434 0.663934 0.648983 0.531229
X6 1.32e-04 2.02e-01 0.847271 0.649539 0.648983 0.683114 0.569006
X7 6.04e-04 1.50e+00 0.650728 0.547968 0.531229 0.569006 3.702975
X8 3.53e-06 2.01e-01 0.182321 0.124043 0.103206 0.118964 0.321120
X8
X1 3.53e-06
X2 2.01e-01
X3 1.82e-01
X4 1.24e-01
X5 1.03e-01
X6 1.19e-01
X7 3.21e-01
X8 1.44e-01
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
lactic 20 2 11 0.359580
Best subsample:
[1] 1 2 3 4 5 7 8 9 10 11 12
Outliers: 4 :
[1] 17 18 19 20
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=11)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 2, 3, 4, 5, 6; C-step iterations: 3, 3, 3, 2, 3, 3
Log(Det.): 0.36
Robust Estimate of Location:
X Y
3.86 5.01
Robust Estimate of Covariance:
X Y
X 10.6 14.6
Y 14.6 21.3
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
pension 18 2 10 16.675508
Best subsample:
[1] 1 2 3 4 5 6 8 9 11 12
Outliers: 5 :
[1] 14 15 16 17 18
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=10)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 2, 3, 4, 5, 6; C-step iterations: 2, 2, 2, 3, 3, 2
Log(Det.): 16.7
Robust Estimate of Location:
Income Reserves
52.3 560.9
Robust Estimate of Covariance:
Income Reserves
Income 1420 11932
Reserves 11932 208643
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
pilot 20 2 11 7.023173
Best subsample:
[1] 1 2 3 4 8 11 12 13 14 15 19
Outliers: 0
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=11)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 2, 3, 4, 5, 6; C-step iterations: 2, 2, 2, 2, 2, 2
Log(Det.): 7.02
Robust Estimate of Location:
X Y
103.0 68.6
Robust Estimate of Covariance:
X Y
X 2581 830
Y 830 268
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
vaso 39 2 21 -3.972244
Best subsample:
[1] 3 4 8 14 18 19 20 21 22 23 24 25 26 27 28 33 34 35 37 38 39
Outliers: 4 :
[1] 1 2 17 31
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=21)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 2, 3, 4, 6; C-step iterations: 3, 3, 3, 2, 2, 3
Log(Det.): -3.97
Robust Estimate of Location:
Volume Rate
1.16 1.72
Robust Estimate of Covariance:
Volume Rate
Volume 0.313 -0.167
Rate -0.167 0.728
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
wagnerGrowth 63 6 35 6.511864
Best subsample:
[1] 2 3 4 5 6 7 9 10 11 12 13 16 17 18 20 23 25 27 31 32 35 36 38 41 44
[26] 48 51 52 53 54 55 56 57 60 62
Outliers: 15 :
[1] 1 8 15 21 22 28 29 33 39 42 43 46 49 50 63
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=35)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 3; C-step iterations: 3, 3, 3, 3, 3, 3
Log(Det.): 6.51
Robust Estimate of Location:
Region PA GPA HS GHS y
10.91 33.65 -2.05 2.43 0.31 6.98
Robust Estimate of Covariance:
Region PA GPA HS GHS y
Region 35.136 17.7291 -1.400 -0.6554 -0.4728 -14.930
PA 17.729 28.4297 -5.525 -1.2444 -0.0452 -29.618
GPA -1.400 -5.5245 5.217 0.3954 -0.2152 3.825
HS -0.655 -1.2444 0.395 0.7273 -0.0107 2.151
GHS -0.473 -0.0452 -0.215 -0.0107 0.1728 0.844
y -14.930 -29.6181 3.825 2.1514 0.8440 79.051
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
fish 158 6 82 8.880459
Best subsample:
[1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
[20] 20 21 22 23 24 25 26 27 35 36 37 42 43 44 45 46 47 48 49
[39] 50 51 52 53 54 55 56 57 58 59 60 106 107 108 109 110 111 112 113
[58] 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132
[77] 134 135 136 137 138 139
Outliers: 64 :
[1] 29 38 39 40 61 62 63 64 65 67 68 69 72 73 74 75 76 77 78
[20] 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97
[39] 98 99 100 101 102 103 104 140 141 142 143 144 145 146 147 148 149 150 151
[58] 152 153 154 155 156 157 158
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=82)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 6; C-step iterations: 7, 7, 7, 5, 6, 6
Log(Det.): 8.88
Robust Estimate of Location:
Weight Length1 Length2 Length3 Height Width
316.3 24.1 26.3 29.3 31.0 14.7
Robust Estimate of Covariance:
Weight Length1 Length2 Length3 Height Width
Weight 64662.2 1412.34 1541.95 1917.21 1420.83 -61.15
Length1 1412.3 34.14 37.04 45.07 29.25 -1.26
Length2 1541.9 37.04 40.26 49.04 32.21 -1.34
Length3 1917.2 45.07 49.04 60.82 43.03 -2.15
Height 1420.8 29.25 32.21 43.03 46.50 -2.66
Width -61.1 -1.26 -1.34 -2.15 -2.66 1.02
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
pottery 27 6 17 -10.586933
Best subsample:
[1] 1 2 4 5 6 9 10 11 13 14 15 19 20 21 22 26 27
Outliers: 9 :
[1] 3 8 12 16 17 18 23 24 25
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=17)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 3; C-step iterations: 2, 2, 2, 2, 2, 2
Log(Det.): -10.6
Robust Estimate of Location:
SI AL FE MG CA TI
54.983 15.206 9.700 3.817 5.211 0.859
Robust Estimate of Covariance:
SI AL FE MG CA TI
SI 20.5823 2.2874 -0.0204 2.1265 -1.8023 0.08821
AL 2.2874 4.0361 -0.6302 -2.4997 0.2084 -0.02038
FE -0.0204 -0.6302 0.2780 0.5338 -0.3512 0.01427
MG 2.1265 -2.4997 0.5338 2.7956 -0.1579 0.02847
CA -1.8023 0.2084 -0.3512 -0.1579 1.2324 -0.03465
TI 0.0882 -0.0204 0.0143 0.0285 -0.0347 0.00175
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
rice 105 6 56 -14.423048
Best subsample:
[1] 4 6 8 10 13 15 16 17 18 25 27 29 30 31 32 33 34 36 37
[20] 38 44 45 47 51 52 53 55 59 60 65 66 67 70 72 74 76 78 79
[39] 80 81 82 83 84 85 86 90 92 93 94 95 97 98 99 100 101 105
Outliers: 13 :
[1] 9 19 28 40 42 43 49 58 62 64 71 75 77
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=56)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1; C-step iterations: 3, 3, 3, 3, 5, 3
Log(Det.): -14.4
Robust Estimate of Location:
Favor Appearance Taste Stickiness
-0.2950 0.0799 -0.1555 0.0363
Toughness Overall_evaluation
0.0530 -0.2284
Robust Estimate of Covariance:
Favor Appearance Taste Stickiness Toughness
Favor 0.466 0.389 0.471 0.447 -0.198
Appearance 0.389 0.610 0.592 0.570 -0.293
Taste 0.471 0.592 0.760 0.718 -0.356
Stickiness 0.447 0.570 0.718 0.820 -0.419
Toughness -0.198 -0.293 -0.356 -0.419 0.400
Overall_evaluation 0.557 0.669 0.838 0.846 -0.425
Overall_evaluation
Favor 0.557
Appearance 0.669
Taste 0.838
Stickiness 0.846
Toughness -0.425
Overall_evaluation 0.987
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
un86 73 7 40 17.117142
Best subsample:
[1] 2 9 10 12 14 16 17 18 19 20 23 24 25 26 27 31 32 33 37 39 42 48 49 50 51
[26] 52 55 56 57 60 61 62 63 64 65 67 70 71 72 73
Outliers: 30 :
[1] 3 4 5 6 7 8 11 13 15 21 22 28 29 30 35 36 38 40 41 43 44 45 46 53 54
[26] 58 59 66 68 69
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=40)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 2, 3, 4, 6; C-step iterations: 3, 2, 3, 3, 2, 3
Log(Det.): 17.1
Robust Estimate of Location:
POP MOR CAR DR GNP DEN TB
17.036 68.512 6.444 0.877 1.134 64.140 0.433
Robust Estimate of Covariance:
POP MOR CAR DR GNP DEN TB
POP 361.0402 195.296 -6.28 -0.0191 -2.06758 57.896 -0.06089
MOR 195.2957 2389.391 -279.44 -33.7257 -33.85782 -920.991 -0.99323
CAR -6.2818 -279.436 57.58 5.7749 6.58636 78.132 0.24976
DR -0.0191 -33.726 5.77 0.9066 0.56604 16.926 0.01980
GNP -2.0676 -33.858 6.59 0.5660 1.42442 9.285 0.00682
DEN 57.8963 -920.991 78.13 16.9262 9.28454 3530.116 -0.97487
TB -0.0609 -0.993 0.25 0.0198 0.00682 -0.975 0.01636
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
wages 36 9 23 25.722758
Best subsample:
[1] 1 2 3 6 7 8 10 11 14 15 17 20 21 22 23 25 27 29 31 33 34 35 36
Outliers: 13 :
[1] 4 5 9 12 13 16 18 19 24 26 28 30 32
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=23)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1; C-step iterations: 2, 2, 2, 2, 2, 2
Log(Det.): 25.7
Robust Estimate of Location:
HRS RATE ERSP ERNO NEIN ASSET AGE DEP
2150.30 2.90 1117.87 306.83 356.52 6861.39 39.32 2.45
SCHOOL
10.24
Robust Estimate of Covariance:
HRS RATE ERSP ERNO NEIN ASSET AGE
HRS 3933.64 15.729 -4649.70 -630.546 6647.3 149167 -3.94e+01
RATE 15.73 0.210 5.82 3.237 49.4 1151 -1.35e-01
ERSP -4649.70 5.816 15177.00 464.307 -4624.8 -90372 5.56e+01
ERNO -630.55 3.237 464.31 2297.265 171.8 3479 1.32e+01
NEIN 6647.32 49.379 -4624.80 171.845 16303.6 365111 -4.96e+01
ASSET 149166.83 1151.179 -90372.14 3478.864 365110.6 8242103 -1.16e+03
AGE -39.36 -0.135 55.58 13.223 -49.6 -1164 7.22e-01
DEP -1.61 -0.071 -17.61 -0.431 -16.4 -366 -7.67e-02
SCHOOL 46.30 0.470 -0.21 2.524 119.8 2788 -4.46e-01
DEP SCHOOL
HRS -1.6112 46.295
RATE -0.0710 0.470
ERSP -17.6121 -0.210
ERNO -0.4309 2.524
NEIN -16.4023 119.836
ASSET -366.3185 2788.094
AGE -0.0767 -0.446
DEP 0.0849 -0.149
SCHOOL -0.1485 1.122
--------------------------------------------------------
========================================================
> ## vvvv no timing for 'R CMD Rdiff' outputs
> doMCDdata(nrep = 12, time=FALSE)
Call: doMCDdata(nrep = 12, time = FALSE)
Data Set n p h(alf) LOG(obj)
=============================================
bushfire 38 5 22 18.135810
Best subsample:
[1] 1 2 3 4 5 6 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Outliers: 16 :
[1] 7 8 9 10 11 12 29 30 31 32 33 34 35 36 37 38
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=22); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 18.1
Robust Estimate of Location:
V1 V2 V3 V4 V5
105 147 274 218 279
Robust Estimate of Covariance:
V1 V2 V3 V4 V5
V1 346 268 -1692 -381 -311
V2 268 236 -1125 -230 -194
V3 -1692 -1125 9993 2455 1951
V4 -381 -230 2455 647 505
V5 -311 -194 1951 505 398
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
heart 12 2 7 5.678742
Best subsample:
[1] 1 3 4 5 7 9 11
Outliers: 0
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=7); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 5.68
Robust Estimate of Location:
height weight
38.3 33.1
Robust Estimate of Covariance:
height weight
height 135 259
weight 259 564
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
starsCYG 47 2 25 -8.031215
Best subsample:
[1] 1 2 4 6 8 10 12 13 16 24 25 26 28 32 33 37 38 39 40 41 42 43 44 45 46
Outliers: 7 :
[1] 7 9 11 14 20 30 34
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=25); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): -8.03
Robust Estimate of Location:
log.Te log.light
4.41 4.95
Robust Estimate of Covariance:
log.Te log.light
log.Te 0.0132 0.0394
log.light 0.0394 0.2743
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
stackloss 21 3 12 5.472581
Best subsample:
[1] 4 5 6 7 8 9 10 11 12 13 14 20
Outliers: 9 :
[1] 1 2 3 15 16 17 18 19 21
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=12); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 5.47
Robust Estimate of Location:
Air.Flow Water.Temp Acid.Conc.
59.5 20.8 87.3
Robust Estimate of Covariance:
Air.Flow Water.Temp Acid.Conc.
Air.Flow 6.29 5.85 5.74
Water.Temp 5.85 9.23 6.14
Acid.Conc. 5.74 6.14 23.25
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
phosphor 18 2 10 6.878847
Best subsample:
[1] 3 5 8 9 11 12 13 14 15 17
Outliers: 3 :
[1] 1 6 10
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=10); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 6.88
Robust Estimate of Location:
inorg organic
13.4 38.8
Robust Estimate of Covariance:
inorg organic
inorg 129 130
organic 130 182
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
coleman 20 5 13 1.286808
Best subsample:
[1] 2 3 4 5 7 8 12 13 14 16 17 19 20
Outliers: 7 :
[1] 1 6 9 10 11 15 18
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=13); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 1.29
Robust Estimate of Location:
salaryP fatherWc sstatus teacherSc motherLev
2.76 48.38 6.12 25.00 6.40
Robust Estimate of Covariance:
salaryP fatherWc sstatus teacherSc motherLev
salaryP 0.253 1.79 -0.266 0.151 0.075
fatherWc 1.786 1303.38 330.496 12.604 34.503
sstatus -0.266 330.50 119.888 3.833 10.131
teacherSc 0.151 12.60 3.833 0.785 0.555
motherLev 0.075 34.50 10.131 0.555 1.043
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
salinity 28 3 16 1.326364
Best subsample:
[1] 1 2 6 7 8 12 13 14 18 20 21 22 25 26 27 28
Outliers: 4 :
[1] 5 16 23 24
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=16); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 1.33
Robust Estimate of Location:
X1 X2 X3
10.08 2.78 22.78
Robust Estimate of Covariance:
X1 X2 X3
X1 10.44 1.01 -3.19
X2 1.01 3.83 -1.44
X3 -3.19 -1.44 2.39
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
wood 20 5 13 -36.270094
Best subsample:
[1] 1 2 3 5 9 10 12 13 14 15 17 18 20
Outliers: 7 :
[1] 4 6 7 8 11 16 19
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=13); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): -36.3
Robust Estimate of Location:
x1 x2 x3 x4 x5
0.587 0.122 0.531 0.538 0.892
Robust Estimate of Covariance:
x1 x2 x3 x4 x5
x1 0.010025 1.88e-03 0.003153 -0.000586 -1.63e-03
x2 0.001881 4.85e-04 0.001269 -0.000052 2.36e-05
x3 0.003153 1.27e-03 0.006632 -0.000871 3.52e-04
x4 -0.000586 -5.20e-05 -0.000871 0.002846 1.83e-03
x5 -0.001630 2.36e-05 0.000352 0.001828 2.77e-03
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
hbk 75 3 39 -1.047858
Best subsample:
[1] 15 16 17 18 19 20 21 22 23 24 26 27 31 32 33 35 36 37 38 40 43 49 50 51 54
[26] 55 56 58 59 61 63 64 66 67 70 71 72 73 74
Outliers: 14 :
[1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=39); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): -1.05
Robust Estimate of Location:
X1 X2 X3
1.54 1.78 1.69
Robust Estimate of Covariance:
X1 X2 X3
X1 1.227 0.055 0.127
X2 0.055 1.249 0.153
X3 0.127 0.153 1.160
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
Animals 28 2 15 14.555543
Best subsample:
[1] 1 3 4 5 10 11 17 18 19 20 21 22 23 26 27
Outliers: 14 :
[1] 2 6 7 8 9 12 13 14 15 16 23 24 25 28
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=15); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 14.6
Robust Estimate of Location:
body brain
18.7 64.9
Robust Estimate of Covariance:
body brain
body 929 1576
brain 1576 5646
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
milk 86 8 47 -28.893938
Best subsample:
[1] 5 7 8 9 10 21 22 24 26 30 31 32 33 34 35 37 38 39 45 46 51 53 54 55 56
[26] 57 58 59 60 61 63 64 65 66 67 68 69 71 72 76 78 79 80 81 83 84 86
Outliers: 21 :
[1] 1 2 3 11 12 13 14 15 16 17 18 20 27 41 44 47 50 70 74 75 77
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=47); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): -28.9
Robust Estimate of Location:
X1 X2 X3 X4 X5 X6 X7 X8
1.03 35.76 33.05 26.12 25.10 25.04 122.94 14.36
Robust Estimate of Covariance:
X1 X2 X3 X4 X5 X6 X7
X1 4.68e-07 8.92e-05 0.00018 0.000172 0.000152 0.000143 0.000625
X2 8.92e-05 1.56e+00 0.21893 0.161497 0.101095 0.197334 1.278580
X3 1.80e-04 2.19e-01 1.17765 0.868701 0.855642 0.864872 0.690044
X4 1.72e-04 1.61e-01 0.86870 0.688578 0.659177 0.660833 0.565031
X5 1.52e-04 1.01e-01 0.85564 0.659177 0.692458 0.667944 0.570607
X6 1.43e-04 1.97e-01 0.86487 0.660833 0.667944 0.693997 0.572373
X7 6.25e-04 1.28e+00 0.69004 0.565031 0.570607 0.572373 3.468208
X8 3.52e-06 1.15e-01 0.17236 0.114700 0.097445 0.107939 0.211966
X8
X1 3.52e-06
X2 1.15e-01
X3 1.72e-01
X4 1.15e-01
X5 9.74e-02
X6 1.08e-01
X7 2.12e-01
X8 1.16e-01
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
lactic 20 2 11 0.359580
Best subsample:
[1] 1 2 3 4 5 7 8 9 10 11 12
Outliers: 4 :
[1] 17 18 19 20
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=11); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 0.36
Robust Estimate of Location:
X Y
3.86 5.01
Robust Estimate of Covariance:
X Y
X 10.6 14.6
Y 14.6 21.3
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
pension 18 2 10 16.675508
Best subsample:
[1] 1 2 3 4 5 6 8 9 11 12
Outliers: 5 :
[1] 14 15 16 17 18
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=10); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 16.7
Robust Estimate of Location:
Income Reserves
52.3 560.9
Robust Estimate of Covariance:
Income Reserves
Income 1420 11932
Reserves 11932 208643
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
pilot 20 2 11 6.487287
Best subsample:
[1] 2 3 6 7 9 12 15 16 17 18 20
Outliers: 0
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=11); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 6.49
Robust Estimate of Location:
X Y
101.1 67.7
Robust Estimate of Covariance:
X Y
X 3344 1070
Y 1070 343
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
vaso 39 2 21 -3.972244
Best subsample:
[1] 3 4 8 14 18 19 20 21 22 23 24 25 26 27 28 33 34 35 37 38 39
Outliers: 4 :
[1] 1 2 17 31
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=21); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): -3.97
Robust Estimate of Location:
Volume Rate
1.16 1.72
Robust Estimate of Covariance:
Volume Rate
Volume 0.313 -0.167
Rate -0.167 0.728
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
wagnerGrowth 63 6 35 6.569262
Best subsample:
[1] 2 3 4 5 6 7 9 10 11 12 14 16 17 18 20 23 25 27 31 32 35 36 38 41 44
[26] 48 52 53 54 55 56 57 58 60 62
Outliers: 17 :
[1] 1 8 15 21 22 24 26 28 29 33 39 42 43 46 50 61 63
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=35); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 6.57
Robust Estimate of Location:
Region PA GPA HS GHS y
11.318 34.050 -2.049 2.498 0.289 6.650
Robust Estimate of Covariance:
Region PA GPA HS GHS y
Region 32.797 14.685 -1.650 -1.0301 -0.2907 -10.601
PA 14.685 25.961 -6.038 -1.5554 0.1318 -25.877
GPA -1.650 -6.038 5.352 0.3838 -0.1690 4.583
HS -1.030 -1.555 0.384 0.9156 -0.0486 3.194
GHS -0.291 0.132 -0.169 -0.0486 0.1205 -0.209
y -10.601 -25.877 4.583 3.1936 -0.2085 70.718
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
fish 158 6 82 8.859084
Best subsample:
[1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
[20] 20 21 22 23 24 25 26 27 28 32 35 36 37 42 43 44 45 46 47
[39] 48 49 50 51 52 53 54 55 56 57 58 59 60 107 109 110 111 112 113
[58] 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132
[77] 134 135 136 137 138 139
Outliers: 63 :
[1] 29 38 39 40 41 61 62 63 64 65 67 68 69 72 73 74 75 76 77
[20] 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96
[39] 97 98 99 100 101 102 103 104 140 142 143 144 146 147 148 149 150 151 152
[58] 153 154 155 156 157 158
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=82); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 8.86
Robust Estimate of Location:
Weight Length1 Length2 Length3 Height Width
329.9 24.5 26.6 29.7 31.1 14.7
Robust Estimate of Covariance:
Weight Length1 Length2 Length3 Height Width
Weight 69083.0 1477.81 1613.6 1992.62 1439.32 -62.12
Length1 1477.8 34.68 37.6 45.51 28.82 -1.31
Length2 1613.6 37.61 40.9 49.52 31.81 -1.40
Length3 1992.6 45.51 49.5 61.16 42.65 -2.25
Height 1439.3 28.82 31.8 42.65 46.74 -2.82
Width -62.1 -1.31 -1.4 -2.25 -2.82 1.01
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
pottery 27 6 17 -10.586933
Best subsample:
[1] 1 2 4 5 6 9 10 11 13 14 15 19 20 21 22 26 27
Outliers: 9 :
[1] 3 8 12 16 17 18 23 24 25
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=17); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): -10.6
Robust Estimate of Location:
SI AL FE MG CA TI
54.983 15.206 9.700 3.817 5.211 0.859
Robust Estimate of Covariance:
SI AL FE MG CA TI
SI 20.5823 2.2874 -0.0204 2.1265 -1.8023 0.08821
AL 2.2874 4.0361 -0.6302 -2.4997 0.2084 -0.02038
FE -0.0204 -0.6302 0.2780 0.5338 -0.3512 0.01427
MG 2.1265 -2.4997 0.5338 2.7956 -0.1579 0.02847
CA -1.8023 0.2084 -0.3512 -0.1579 1.2324 -0.03465
TI 0.0882 -0.0204 0.0143 0.0285 -0.0347 0.00175
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
rice 105 6 56 -14.463986
Best subsample:
[1] 2 4 6 8 10 12 15 18 21 22 24 29 30 31 32 33 34 36 37
[20] 38 41 44 45 47 51 52 53 54 55 59 61 65 67 68 69 70 72 76
[39] 78 79 80 81 82 83 84 85 86 92 93 94 95 97 98 99 102 105
Outliers: 13 :
[1] 9 14 19 28 40 42 49 58 62 71 75 77 89
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=56); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): -14.5
Robust Estimate of Location:
Favor Appearance Taste Stickiness
-0.2731 0.0600 -0.1468 0.0646
Toughness Overall_evaluation
0.0894 -0.2192
Robust Estimate of Covariance:
Favor Appearance Taste Stickiness Toughness
Favor 0.388 0.323 0.393 0.389 -0.195
Appearance 0.323 0.503 0.494 0.494 -0.270
Taste 0.393 0.494 0.640 0.629 -0.361
Stickiness 0.389 0.494 0.629 0.815 -0.486
Toughness -0.195 -0.270 -0.361 -0.486 0.451
Overall_evaluation 0.471 0.575 0.723 0.772 -0.457
Overall_evaluation
Favor 0.471
Appearance 0.575
Taste 0.723
Stickiness 0.772
Toughness -0.457
Overall_evaluation 0.882
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
un86 73 7 40 16.965868
Best subsample:
[1] 1 9 10 12 14 16 17 18 20 23 24 26 27 31 32 33 37 39 42 45 47 48 49 50 51
[26] 52 55 56 57 60 61 62 63 64 65 67 70 71 72 73
Outliers: 31 :
[1] 3 4 5 6 7 8 11 13 15 19 21 22 25 28 29 30 34 35 36 38 40 43 44 46 53
[26] 54 58 59 66 68 69
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=40); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 17
Robust Estimate of Location:
POP MOR CAR DR GNP DEN TB
21.110 70.143 6.581 0.834 1.169 53.692 0.444
Robust Estimate of Covariance:
POP MOR CAR DR GNP DEN TB
POP 589.850 246.49 -15.648 -2.0167 -3.86409 287.611 0.34871
MOR 246.492 2370.52 -287.608 -32.1359 -35.44415 -673.259 -1.06385
CAR -15.648 -287.61 58.485 5.7597 6.63441 107.711 0.25254
DR -2.017 -32.14 5.760 0.8406 0.59370 14.998 0.01685
GNP -3.864 -35.44 6.634 0.5937 1.42649 16.827 0.00217
DEN 287.611 -673.26 107.711 14.9975 16.82656 1629.056 -0.45076
TB 0.349 -1.06 0.253 0.0169 0.00217 -0.451 0.01829
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
wages 36 9 23 25.781100
Best subsample:
[1] 1 2 3 6 7 8 9 10 11 14 17 18 20 21 22 23 25 26 27 33 34 35 36
Outliers: 13 :
[1] 4 5 12 13 15 16 19 24 28 29 30 31 32
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=23); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x)
Log(Det.): 25.8
Robust Estimate of Location:
HRS RATE ERSP ERNO NEIN ASSET AGE DEP
2150.65 2.82 1135.17 293.00 345.61 6552.57 39.44 2.39
SCHOOL
10.09
Robust Estimate of Covariance:
HRS RATE ERSP ERNO NEIN ASSET
HRS 6092.92 15.1803 -2410.41 -2.40e+03 8807.1 193759
RATE 15.18 0.2017 10.24 -9.14e-01 49.0 1142
ERSP -2410.41 10.2403 13932.45 5.36e+02 -3271.0 -55432
ERNO -2397.41 -0.9137 535.75 2.36e+03 -2020.8 -44920
NEIN 8807.14 48.9680 -3271.05 -2.02e+03 18314.6 409392
ASSET 193758.66 1142.4445 -55432.35 -4.49e+04 409392.2 9215780
AGE -63.71 -0.1916 15.01 3.02e+01 -95.6 -2149
DEP -9.89 -0.0562 -9.65 4.99e+00 -16.7 -374
SCHOOL 62.36 0.4612 23.49 -1.68e+01 136.8 3150
AGE DEP SCHOOL
HRS -6.37e+01 -9.8883 62.357
RATE -1.92e-01 -0.0562 0.461
ERSP 1.50e+01 -9.6481 23.487
ERNO 3.02e+01 4.9941 -16.814
NEIN -9.56e+01 -16.6945 136.752
ASSET -2.15e+03 -373.6149 3150.225
AGE 9.46e-01 0.0972 -0.765
DEP 9.72e-02 0.0580 -0.169
SCHOOL -7.65e-01 -0.1688 1.256
--------------------------------------------------------
========================================================
> doMCDdata(nrep = 12, time=FALSE, method="DetMCD"); warnings()
Call: doMCDdata(nrep = 12, time = FALSE, method = "DetMCD")
Data Set n p h(alf) LOG(obj)
=============================================
bushfire 38 5 22 18.135810
Best subsample:
[1] 1 2 3 4 5 6 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Outliers: 16 :
[1] 7 8 9 10 11 12 29 30 31 32 33 34 35 36 37 38
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=22)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 2, 3, 6; C-step iterations: 2, 3, 3, 2, 2, 3
Log(Det.): 18.1
Robust Estimate of Location:
V1 V2 V3 V4 V5
105 147 274 218 279
Robust Estimate of Covariance:
V1 V2 V3 V4 V5
V1 346 268 -1692 -381 -311
V2 268 236 -1125 -230 -194
V3 -1692 -1125 9993 2455 1951
V4 -381 -230 2455 647 505
V5 -311 -194 1951 505 398
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
heart 12 2 7 5.678742
Best subsample:
[1] 1 3 4 5 7 9 11
Outliers: 0
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=7)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 2, 3, 4, 6; C-step iterations: 2, 2, 2, 2, 2, 2
Log(Det.): 5.68
Robust Estimate of Location:
height weight
38.3 33.1
Robust Estimate of Covariance:
height weight
height 135 259
weight 259 564
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
starsCYG 47 2 25 -8.028718
Best subsample:
[1] 1 6 10 12 13 16 23 24 25 26 28 31 32 33 37 38 39 40 41 42 43 44 45 46 47
Outliers: 7 :
[1] 7 9 11 14 20 30 34
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=25)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 5; C-step iterations: 4, 4, 4, 4, 4, 4
Log(Det.): -8.03
Robust Estimate of Location:
log.Te log.light
4.41 4.95
Robust Estimate of Covariance:
log.Te log.light
log.Te 0.0132 0.0394
log.light 0.0394 0.2743
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
stackloss 21 3 12 6.577286
Best subsample:
[1] 4 5 6 7 8 9 11 13 16 18 19 20
Outliers: 2 :
[1] 1 2
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=12)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 6; C-step iterations: 3, 3, 3, 3, 2, 2
Log(Det.): 6.58
Robust Estimate of Location:
Air.Flow Water.Temp Acid.Conc.
58.4 20.5 86.1
Robust Estimate of Covariance:
Air.Flow Water.Temp Acid.Conc.
Air.Flow 56.3 13.33 26.68
Water.Temp 13.3 8.28 6.98
Acid.Conc. 26.7 6.98 37.97
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
phosphor 18 2 10 7.732906
Best subsample:
[1] 2 4 5 7 8 9 11 12 14 16
Outliers: 1 :
[1] 6
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=10)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 4; C-step iterations: 3, 3, 3, 3, 3, 3
Log(Det.): 7.73
Robust Estimate of Location:
inorg organic
12.5 40.8
Robust Estimate of Covariance:
inorg organic
inorg 124 101
organic 101 197
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
coleman 20 5 13 2.149184
Best subsample:
[1] 3 4 5 7 8 12 13 14 16 17 18 19 20
Outliers: 2 :
[1] 6 10
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=13)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 5; C-step iterations: 2, 2, 2, 2, 2, 3
Log(Det.): 2.15
Robust Estimate of Location:
salaryP fatherWc sstatus teacherSc motherLev
2.76 41.08 2.76 25.01 6.27
Robust Estimate of Covariance:
salaryP fatherWc sstatus teacherSc motherLev
salaryP 0.391 2.96 2.15 0.447 0.110
fatherWc 2.956 1358.64 442.72 12.235 32.842
sstatus 2.146 442.72 205.59 6.464 11.382
teacherSc 0.447 12.23 6.46 1.179 0.510
motherLev 0.110 32.84 11.38 0.510 0.919
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
salinity 28 3 16 1.940763
Best subsample:
[1] 1 8 10 12 13 14 15 17 18 20 21 22 25 26 27 28
Outliers: 2 :
[1] 5 16
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=16)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 4, 5; C-step iterations: 2, 2, 2, 3, 2, 2
Log(Det.): 1.94
Robust Estimate of Location:
X1 X2 X3
10.50 2.58 23.12
Robust Estimate of Covariance:
X1 X2 X3
X1 10.90243 -0.00457 -1.46
X2 -0.00457 3.85051 -1.95
X3 -1.46156 -1.94604 3.21
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
wood 20 5 13 -35.240819
Best subsample:
[1] 1 2 3 5 9 11 12 13 14 15 17 18 20
Outliers: 4 :
[1] 4 6 8 19
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=13)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 2; C-step iterations: 2, 2, 2, 2, 2, 2
Log(Det.): -35.2
Robust Estimate of Location:
x1 x2 x3 x4 x5
0.582 0.125 0.530 0.534 0.888
Robust Estimate of Covariance:
x1 x2 x3 x4 x5
x1 0.010502 0.001810 2.08e-03 -0.000641 -9.61e-04
x2 0.001810 0.000555 8.76e-04 -0.000203 -4.70e-05
x3 0.002081 0.000876 5.60e-03 -0.001106 -1.26e-05
x4 -0.000641 -0.000203 -1.11e-03 0.004266 2.60e-03
x5 -0.000961 -0.000047 -1.26e-05 0.002602 2.95e-03
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
hbk 75 3 39 -1.045501
Best subsample:
[1] 15 17 18 19 20 21 22 23 24 26 27 28 29 32 33 35 36 38 40 41 43 48 49 50 51
[26] 54 55 56 58 59 63 64 66 67 70 71 72 73 74
Outliers: 14 :
[1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=39)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 2, 3, 4, 6; C-step iterations: 5, 5, 5, 5, 4, 5
Log(Det.): -1.05
Robust Estimate of Location:
X1 X2 X3
1.54 1.78 1.69
Robust Estimate of Covariance:
X1 X2 X3
X1 1.227 0.055 0.127
X2 0.055 1.249 0.153
X3 0.127 0.153 1.160
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
Animals 28 2 15 14.555543
Best subsample:
[1] 1 3 4 5 10 11 17 18 19 20 21 22 23 26 27
Outliers: 14 :
[1] 2 6 7 8 9 12 13 14 15 16 23 24 25 28
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=15)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 2, 3, 4, 5, 6; C-step iterations: 2, 2, 2, 2, 2, 2
Log(Det.): 14.6
Robust Estimate of Location:
body brain
18.7 64.9
Robust Estimate of Covariance:
body brain
body 929 1576
brain 1576 5646
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
milk 86 8 47 -28.844954
Best subsample:
[1] 5 8 9 10 21 22 23 24 26 30 31 32 33 34 35 36 37 38 39 46 51 53 54 55 56
[26] 57 58 59 60 61 62 63 64 65 66 67 68 69 71 72 76 78 79 81 83 84 86
Outliers: 20 :
[1] 1 2 3 11 12 13 14 15 16 17 18 20 27 41 44 47 70 74 75 77
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=47)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 5; C-step iterations: 3, 3, 4, 3, 3, 4
Log(Det.): -28.8
Robust Estimate of Location:
X1 X2 X3 X4 X5 X6 X7 X8
1.03 35.90 33.10 26.16 25.13 25.07 123.13 14.39
Robust Estimate of Covariance:
X1 X2 X3 X4 X5 X6 X7
X1 4.62e-07 8.16e-05 0.000162 0.000159 0.000141 0.000132 0.000604
X2 8.16e-05 1.73e+00 0.199526 0.156489 0.081711 0.201994 1.499551
X3 1.62e-04 2.00e-01 1.148093 0.849962 0.824682 0.847271 0.650728
X4 1.59e-04 1.56e-01 0.849962 0.676140 0.638434 0.649539 0.547968
X5 1.41e-04 8.17e-02 0.824682 0.638434 0.663934 0.648983 0.531229
X6 1.32e-04 2.02e-01 0.847271 0.649539 0.648983 0.683114 0.569006
X7 6.04e-04 1.50e+00 0.650728 0.547968 0.531229 0.569006 3.702975
X8 3.53e-06 2.01e-01 0.182321 0.124043 0.103206 0.118964 0.321120
X8
X1 3.53e-06
X2 2.01e-01
X3 1.82e-01
X4 1.24e-01
X5 1.03e-01
X6 1.19e-01
X7 3.21e-01
X8 1.44e-01
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
lactic 20 2 11 0.359580
Best subsample:
[1] 1 2 3 4 5 7 8 9 10 11 12
Outliers: 4 :
[1] 17 18 19 20
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=11)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 2, 3, 4, 5, 6; C-step iterations: 3, 3, 3, 2, 3, 3
Log(Det.): 0.36
Robust Estimate of Location:
X Y
3.86 5.01
Robust Estimate of Covariance:
X Y
X 10.6 14.6
Y 14.6 21.3
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
pension 18 2 10 16.675508
Best subsample:
[1] 1 2 3 4 5 6 8 9 11 12
Outliers: 5 :
[1] 14 15 16 17 18
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=10)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 2, 3, 4, 5, 6; C-step iterations: 2, 2, 2, 3, 3, 2
Log(Det.): 16.7
Robust Estimate of Location:
Income Reserves
52.3 560.9
Robust Estimate of Covariance:
Income Reserves
Income 1420 11932
Reserves 11932 208643
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
pilot 20 2 11 7.023173
Best subsample:
[1] 1 2 3 4 8 11 12 13 14 15 19
Outliers: 0
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=11)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 2, 3, 4, 5, 6; C-step iterations: 2, 2, 2, 2, 2, 2
Log(Det.): 7.02
Robust Estimate of Location:
X Y
103.0 68.6
Robust Estimate of Covariance:
X Y
X 2581 830
Y 830 268
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
vaso 39 2 21 -3.972244
Best subsample:
[1] 3 4 8 14 18 19 20 21 22 23 24 25 26 27 28 33 34 35 37 38 39
Outliers: 4 :
[1] 1 2 17 31
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=21)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 2, 3, 4, 6; C-step iterations: 3, 3, 3, 2, 2, 3
Log(Det.): -3.97
Robust Estimate of Location:
Volume Rate
1.16 1.72
Robust Estimate of Covariance:
Volume Rate
Volume 0.313 -0.167
Rate -0.167 0.728
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
wagnerGrowth 63 6 35 6.511864
Best subsample:
[1] 2 3 4 5 6 7 9 10 11 12 13 16 17 18 20 23 25 27 31 32 35 36 38 41 44
[26] 48 51 52 53 54 55 56 57 60 62
Outliers: 15 :
[1] 1 8 15 21 22 28 29 33 39 42 43 46 49 50 63
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=35)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 3; C-step iterations: 3, 3, 3, 3, 3, 3
Log(Det.): 6.51
Robust Estimate of Location:
Region PA GPA HS GHS y
10.91 33.65 -2.05 2.43 0.31 6.98
Robust Estimate of Covariance:
Region PA GPA HS GHS y
Region 35.136 17.7291 -1.400 -0.6554 -0.4728 -14.930
PA 17.729 28.4297 -5.525 -1.2444 -0.0452 -29.618
GPA -1.400 -5.5245 5.217 0.3954 -0.2152 3.825
HS -0.655 -1.2444 0.395 0.7273 -0.0107 2.151
GHS -0.473 -0.0452 -0.215 -0.0107 0.1728 0.844
y -14.930 -29.6181 3.825 2.1514 0.8440 79.051
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
fish 158 6 82 8.880459
Best subsample:
[1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
[20] 20 21 22 23 24 25 26 27 35 36 37 42 43 44 45 46 47 48 49
[39] 50 51 52 53 54 55 56 57 58 59 60 106 107 108 109 110 111 112 113
[58] 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132
[77] 134 135 136 137 138 139
Outliers: 64 :
[1] 29 38 39 40 61 62 63 64 65 67 68 69 72 73 74 75 76 77 78
[20] 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97
[39] 98 99 100 101 102 103 104 140 141 142 143 144 145 146 147 148 149 150 151
[58] 152 153 154 155 156 157 158
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=82)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 6; C-step iterations: 7, 7, 7, 5, 6, 6
Log(Det.): 8.88
Robust Estimate of Location:
Weight Length1 Length2 Length3 Height Width
316.3 24.1 26.3 29.3 31.0 14.7
Robust Estimate of Covariance:
Weight Length1 Length2 Length3 Height Width
Weight 64662.2 1412.34 1541.95 1917.21 1420.83 -61.15
Length1 1412.3 34.14 37.04 45.07 29.25 -1.26
Length2 1541.9 37.04 40.26 49.04 32.21 -1.34
Length3 1917.2 45.07 49.04 60.82 43.03 -2.15
Height 1420.8 29.25 32.21 43.03 46.50 -2.66
Width -61.1 -1.26 -1.34 -2.15 -2.66 1.02
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
pottery 27 6 17 -10.586933
Best subsample:
[1] 1 2 4 5 6 9 10 11 13 14 15 19 20 21 22 26 27
Outliers: 9 :
[1] 3 8 12 16 17 18 23 24 25
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=17)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 3; C-step iterations: 2, 2, 2, 2, 2, 2
Log(Det.): -10.6
Robust Estimate of Location:
SI AL FE MG CA TI
54.983 15.206 9.700 3.817 5.211 0.859
Robust Estimate of Covariance:
SI AL FE MG CA TI
SI 20.5823 2.2874 -0.0204 2.1265 -1.8023 0.08821
AL 2.2874 4.0361 -0.6302 -2.4997 0.2084 -0.02038
FE -0.0204 -0.6302 0.2780 0.5338 -0.3512 0.01427
MG 2.1265 -2.4997 0.5338 2.7956 -0.1579 0.02847
CA -1.8023 0.2084 -0.3512 -0.1579 1.2324 -0.03465
TI 0.0882 -0.0204 0.0143 0.0285 -0.0347 0.00175
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
rice 105 6 56 -14.423048
Best subsample:
[1] 4 6 8 10 13 15 16 17 18 25 27 29 30 31 32 33 34 36 37
[20] 38 44 45 47 51 52 53 55 59 60 65 66 67 70 72 74 76 78 79
[39] 80 81 82 83 84 85 86 90 92 93 94 95 97 98 99 100 101 105
Outliers: 13 :
[1] 9 19 28 40 42 43 49 58 62 64 71 75 77
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=56)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1; C-step iterations: 3, 3, 3, 3, 5, 3
Log(Det.): -14.4
Robust Estimate of Location:
Favor Appearance Taste Stickiness
-0.2950 0.0799 -0.1555 0.0363
Toughness Overall_evaluation
0.0530 -0.2284
Robust Estimate of Covariance:
Favor Appearance Taste Stickiness Toughness
Favor 0.466 0.389 0.471 0.447 -0.198
Appearance 0.389 0.610 0.592 0.570 -0.293
Taste 0.471 0.592 0.760 0.718 -0.356
Stickiness 0.447 0.570 0.718 0.820 -0.419
Toughness -0.198 -0.293 -0.356 -0.419 0.400
Overall_evaluation 0.557 0.669 0.838 0.846 -0.425
Overall_evaluation
Favor 0.557
Appearance 0.669
Taste 0.838
Stickiness 0.846
Toughness -0.425
Overall_evaluation 0.987
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
un86 73 7 40 17.117142
Best subsample:
[1] 2 9 10 12 14 16 17 18 19 20 23 24 25 26 27 31 32 33 37 39 42 48 49 50 51
[26] 52 55 56 57 60 61 62 63 64 65 67 70 71 72 73
Outliers: 30 :
[1] 3 4 5 6 7 8 11 13 15 21 22 28 29 30 35 36 38 40 41 43 44 45 46 53 54
[26] 58 59 66 68 69
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=40)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1, 2, 3, 4, 6; C-step iterations: 3, 2, 3, 3, 2, 3
Log(Det.): 17.1
Robust Estimate of Location:
POP MOR CAR DR GNP DEN TB
17.036 68.512 6.444 0.877 1.134 64.140 0.433
Robust Estimate of Covariance:
POP MOR CAR DR GNP DEN TB
POP 361.0402 195.296 -6.28 -0.0191 -2.06758 57.896 -0.06089
MOR 195.2957 2389.391 -279.44 -33.7257 -33.85782 -920.991 -0.99323
CAR -6.2818 -279.436 57.58 5.7749 6.58636 78.132 0.24976
DR -0.0191 -33.726 5.77 0.9066 0.56604 16.926 0.01980
GNP -2.0676 -33.858 6.59 0.5660 1.42442 9.285 0.00682
DEN 57.8963 -920.991 78.13 16.9262 9.28454 3530.116 -0.97487
TB -0.0609 -0.993 0.25 0.0198 0.00682 -0.975 0.01636
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
wages 36 9 23 25.722758
Best subsample:
[1] 1 2 3 6 7 8 10 11 14 15 17 20 21 22 23 25 27 29 31 33 34 35 36
Outliers: 13 :
[1] 4 5 9 12 13 16 18 19 24 26 28 30 32
------------- *MCD() result: --------------------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=23)
Call:
covMcd(x = x, nsamp = "deterministic")
iBest: 1; C-step iterations: 2, 2, 2, 2, 2, 2
Log(Det.): 25.7
Robust Estimate of Location:
HRS RATE ERSP ERNO NEIN ASSET AGE DEP
2150.30 2.90 1117.87 306.83 356.52 6861.39 39.32 2.45
SCHOOL
10.24
Robust Estimate of Covariance:
HRS RATE ERSP ERNO NEIN ASSET AGE
HRS 3933.64 15.729 -4649.70 -630.546 6647.3 149167 -3.94e+01
RATE 15.73 0.210 5.82 3.237 49.4 1151 -1.35e-01
ERSP -4649.70 5.816 15177.00 464.307 -4624.8 -90372 5.56e+01
ERNO -630.55 3.237 464.31 2297.265 171.8 3479 1.32e+01
NEIN 6647.32 49.379 -4624.80 171.845 16303.6 365111 -4.96e+01
ASSET 149166.83 1151.179 -90372.14 3478.864 365110.6 8242103 -1.16e+03
AGE -39.36 -0.135 55.58 13.223 -49.6 -1164 7.22e-01
DEP -1.61 -0.071 -17.61 -0.431 -16.4 -366 -7.67e-02
SCHOOL 46.30 0.470 -0.21 2.524 119.8 2788 -4.46e-01
DEP SCHOOL
HRS -1.6112 46.295
RATE -0.0710 0.470
ERSP -17.6121 -0.210
ERNO -0.4309 2.524
NEIN -16.4023 119.836
ASSET -366.3185 2788.094
AGE -0.0767 -0.446
DEP 0.0849 -0.149
SCHOOL -0.1485 1.122
--------------------------------------------------------
========================================================
> doMCDdata(nrep = 12, time=FALSE, method = "MASS")
Call: doMCDdata(nrep = 12, time = FALSE, method = "MASS")
Data Set n p h(alf) LOG(obj)
=============================================
bushfire 38 5 22 18.135810
Best subsample:
[1] 1 2 3 4 5 6 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Outliers: 0
------------- *MCD() result: --------------------------
$center
V1 V2 V3 V4 V5
109.44 149.56 260.32 215.12 276.88
$cov
V1 V2 V3 V4 V5
V1 376.67 280.03 -1628.02 -342.01 -285.07
V2 280.03 236.42 -987.14 -188.82 -162.89
V3 -1628.02 -987.14 10203.64 2369.63 1917.58
V4 -342.01 -188.82 2369.63 589.94 468.56
V5 -285.07 -162.89 1917.58 468.56 375.19
$msg
[1] "0 singular samples of size 6 out of 3000"
$crit
[1] 18.136
$best
[1] 1 2 3 4 5 6 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
$n.obs
[1] 38
$quan
[1] 22
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
heart 12 2 7 5.678742
Best subsample:
[1] 1 3 4 5 7 9 11
Outliers: 0
------------- *MCD() result: --------------------------
$center
height weight
40.358 38.125
$cov
height weight
height 142.46 298.91
weight 298.91 679.01
$msg
[1] "0 singular samples of size 3 out of 220"
$crit
[1] 5.6787
$best
[1] 1 3 4 5 7 9 11
$n.obs
[1] 12
$quan
[1] 7
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
starsCYG 47 2 25 -8.031215
Best subsample:
[1] 1 2 4 6 8 10 12 13 16 24 25 26 28 32 33 37 38 39 40 41 42 43 44 45 46
Outliers: 0
------------- *MCD() result: --------------------------
$center
log.Te log.light
4.409 4.949
$cov
log.Te log.light
log.Te 0.011789 0.035179
log.light 0.035179 0.244869
$msg
[1] "12 singular samples of size 3 out of 1500"
$crit
[1] -8.0312
$best
[1] 1 2 4 6 8 10 12 13 16 24 25 26 28 32 33 37 38 39 40 41 42 43 44 45 46
$n.obs
[1] 47
$quan
[1] 25
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
stackloss 21 3 12 5.472581
Best subsample:
[1] 4 5 6 7 8 9 10 11 12 13 14 20
Outliers: 0
------------- *MCD() result: --------------------------
$center
Air.Flow Water.Temp Acid.Conc.
56.706 20.235 85.529
$cov
Air.Flow Water.Temp Acid.Conc.
Air.Flow 23.4706 7.5735 16.1029
Water.Temp 7.5735 6.3162 5.3676
Acid.Conc. 16.1029 5.3676 32.3897
$msg
[1] "88 singular samples of size 4 out of 2000"
$crit
[1] 5.4726
$best
[1] 4 5 6 7 8 9 10 11 12 13 14 20
$n.obs
[1] 21
$quan
[1] 12
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
phosphor 18 2 10 6.878847
Best subsample:
[1] 3 5 8 9 11 12 13 14 15 17
Outliers: 0
------------- *MCD() result: --------------------------
$center
inorg organic
15.215 39.385
$cov
inorg organic
inorg 95.47 116.49
organic 116.49 171.76
$msg
[1] "1 singular samples of size 3 out of 816"
$crit
[1] 6.8788
$best
[1] 3 5 8 9 11 12 13 14 15 17
$n.obs
[1] 18
$quan
[1] 10
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
coleman 20 5 13 1.286808
Best subsample:
[1] 2 3 4 5 7 8 12 13 14 16 17 19 20
Outliers: 0
------------- *MCD() result: --------------------------
$center
salaryP fatherWc sstatus teacherSc motherLev
2.8253 44.6267 4.7133 25.1240 6.3320
$cov
salaryP fatherWc sstatus teacherSc motherLev
salaryP 0.18916 -0.30888 0.14262 0.17971 0.02461
fatherWc -0.30888 683.87325 196.89588 3.30523 17.29381
sstatus 0.14262 196.89588 85.94311 1.68507 5.58631
teacherSc 0.17971 3.30523 1.68507 0.51571 0.21891
motherLev 0.02461 17.29381 5.58631 0.21891 0.50172
$msg
[1] "0 singular samples of size 6 out of 3000"
$crit
[1] 1.2868
$best
[1] 2 3 4 5 7 8 12 13 14 16 17 19 20
$n.obs
[1] 20
$quan
[1] 13
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
salinity 28 3 16 1.326364
Best subsample:
[1] 1 2 6 7 8 12 13 14 18 20 21 22 25 26 27 28
Outliers: 0
------------- *MCD() result: --------------------------
$center
X1 X2 X3
10.0826 2.7826 22.7777
$cov
X1 X2 X3
X1 9.14332 0.88241 -2.7916
X2 0.88241 3.35968 -1.2622
X3 -2.79160 -1.26222 2.0924
$msg
[1] "9 singular samples of size 4 out of 2000"
$crit
[1] 1.3264
$best
[1] 1 2 6 7 8 12 13 14 18 20 21 22 25 26 27 28
$n.obs
[1] 28
$quan
[1] 16
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
wood 20 5 13 -36.270094
Best subsample:
[1] 1 2 3 5 9 10 12 13 14 15 17 18 20
Outliers: 0
------------- *MCD() result: --------------------------
$center
x1 x2 x3 x4 x5
0.57613 0.12294 0.53127 0.53760 0.88913
$cov
x1 x2 x3 x4 x5
x1 5.2757e-03 7.8749e-04 1.2965e-03 -2.0514e-05 -4.0002e-04
x2 7.8749e-04 2.2023e-04 5.4362e-04 2.3846e-05 2.7230e-05
x3 1.2965e-03 5.4362e-04 3.0435e-03 -7.0560e-04 -4.4395e-05
x4 -2.0514e-05 2.3846e-05 -7.0560e-04 2.1388e-03 1.3511e-03
x5 -4.0002e-04 2.7230e-05 -4.4395e-05 1.3511e-03 1.5946e-03
$msg
[1] "0 singular samples of size 6 out of 3000"
$crit
[1] -36.27
$best
[1] 1 2 3 5 9 10 12 13 14 15 17 18 20
$n.obs
[1] 20
$quan
[1] 13
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
hbk 75 3 39 -1.047858
Best subsample:
[1] 15 16 17 18 19 20 21 22 23 24 26 27 31 32 33 35 36 37 38 40 43 49 50 51 54
[26] 55 56 58 59 61 63 64 66 67 70 71 72 73 74
Outliers: 0
------------- *MCD() result: --------------------------
$center
X1 X2 X3
1.5583 1.8033 1.6600
$cov
X1 X2 X3
X1 1.124845 0.022175 0.15373
X2 0.022175 1.138972 0.18149
X3 0.153729 0.181492 1.04346
$msg
[1] "0 singular samples of size 4 out of 2000"
$crit
[1] -1.0479
$best
[1] 15 16 17 18 19 20 21 22 23 24 26 27 31 32 33 35 36 37 38 40 43 49 50 51 54
[26] 55 56 58 59 61 63 64 66 67 70 71 72 73 74
$n.obs
[1] 75
$quan
[1] 39
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
Animals 28 2 15 14.555543
Best subsample:
[1] 1 3 4 5 10 11 17 18 19 20 21 22 23 26 27
Outliers: 0
------------- *MCD() result: --------------------------
$center
body brain
48.331 127.321
$cov
body brain
body 4978.6 7801.4
brain 7801.4 21693.7
$msg
[1] "0 singular samples of size 3 out of 3276"
$crit
[1] 14.556
$best
[1] 1 3 4 5 10 11 17 18 19 20 21 22 23 26 27
$n.obs
[1] 28
$quan
[1] 15
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
milk 86 8 47 -28.931843
Best subsample:
[1] 5 8 9 10 22 23 24 26 30 31 32 33 34 35 37 38 39 45 46 51 53 54 55 56 57
[26] 58 59 60 61 63 64 65 66 67 68 69 71 72 76 78 79 81 83 84 86
Outliers: 0
------------- *MCD() result: --------------------------
$center
X1 X2 X3 X4 X5 X6 X7 X8
1.0302 35.7571 33.0540 26.1206 25.1000 25.0365 122.9397 14.3559
$cov
X1 X2 X3 X4 X5 X6 X7
X1 4.2168e-07 8.0438e-05 0.00016232 0.00015533 0.00013742 0.00012898 0.00056354
X2 8.0438e-05 1.4057e+00 0.19735023 0.14557604 0.09112903 0.17788018 1.15253456
X3 1.6232e-04 1.9735e-01 1.06155658 0.78306196 0.77129032 0.77961086 0.62201741
X4 1.5533e-04 1.4558e-01 0.78306196 0.62069636 0.59419355 0.59568612 0.50932924
X5 1.3742e-04 9.1129e-02 0.77129032 0.59419355 0.62419355 0.60209677 0.51435484
X6 1.2898e-04 1.7788e-01 0.77961086 0.59568612 0.60209677 0.62558116 0.51594726
X7 5.6354e-04 1.1525e+00 0.62201741 0.50932924 0.51435484 0.51594726 3.12630312
X8 3.1754e-06 1.0393e-01 0.15537148 0.10339299 0.08783871 0.09729826 0.19106964
X8
X1 3.1754e-06
X2 1.0393e-01
X3 1.5537e-01
X4 1.0339e-01
X5 8.7839e-02
X6 9.7298e-02
X7 1.9107e-01
X8 1.0417e-01
$msg
[1] "30 singular samples of size 9 out of 3000"
$crit
[1] -28.932
$best
[1] 5 8 9 10 22 23 24 26 30 31 32 33 34 35 37 38 39 45 46 51 53 54 55 56 57
[26] 58 59 60 61 63 64 65 66 67 68 69 71 72 76 78 79 81 83 84 86
$n.obs
[1] 86
$quan
[1] 47
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
lactic 20 2 11 0.359580
Best subsample:
[1] 1 2 3 4 5 7 8 9 10 11 12
Outliers: 0
------------- *MCD() result: --------------------------
$center
X Y
4.625 5.925
$cov
X Y
X 12.117 15.843
Y 15.843 21.705
$msg
[1] "23 singular samples of size 3 out of 1140"
$crit
[1] 0.35958
$best
[1] 1 2 3 4 5 7 8 9 10 11 12
$n.obs
[1] 20
$quan
[1] 11
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
pension 18 2 10 16.675508
Best subsample:
[1] 1 2 3 4 5 6 8 9 11 12
Outliers: 0
------------- *MCD() result: --------------------------
$center
Income Reserves
59.371 671.279
$cov
Income Reserves
Income 1787.4 20057
Reserves 20056.9 329315
$msg
[1] "0 singular samples of size 3 out of 816"
$crit
[1] 16.676
$best
[1] 1 2 3 4 5 6 8 9 11 12
$n.obs
[1] 18
$quan
[1] 10
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
pilot 20 2 11 6.487287
Best subsample:
[1] 2 3 6 7 9 12 15 16 17 18 20
Outliers: 0
------------- *MCD() result: --------------------------
$center
X Y
97.647 66.529
$cov
X Y
X 2761.49 876.45
Y 876.45 279.01
$msg
[1] "21 singular samples of size 3 out of 1140"
$crit
[1] 6.4873
$best
[1] 2 3 6 7 9 12 15 16 17 18 20
$n.obs
[1] 20
$quan
[1] 11
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
vaso 39 2 21 -3.972244
Best subsample:
[1] 3 4 8 14 18 19 20 21 22 23 24 25 26 27 28 33 34 35 37 38 39
Outliers: 0
------------- *MCD() result: --------------------------
$center
Volume Rate
1.2528 1.6717
$cov
Volume Rate
Volume 0.41213 -0.19935
Rate -0.19935 0.68865
$msg
[1] "12 singular samples of size 3 out of 1500"
$crit
[1] -3.9722
$best
[1] 3 4 8 14 18 19 20 21 22 23 24 25 26 27 28 33 34 35 37 38 39
$n.obs
[1] 39
$quan
[1] 21
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
wagnerGrowth 63 6 35 6.511864
Best subsample:
[1] 2 3 4 5 6 7 9 10 11 12 13 16 17 18 20 23 25 27 31 32 35 36 38 41 44
[26] 48 51 52 53 54 55 56 57 60 62
Outliers: 0
------------- *MCD() result: --------------------------
$center
Region PA GPA HS GHS y
10.91837 33.63327 -1.99857 2.49347 0.34224 7.59102
$cov
Region PA GPA HS GHS y
Region 31.32653 15.7286054 -0.47426 -0.891794 -0.3977296 -12.67116
PA 15.72861 24.2037016 -4.27558 -1.253049 -0.0075054 -25.15602
GPA -0.47426 -4.2755818 4.65617 0.236160 -0.1258220 3.50016
HS -0.89179 -1.2530491 0.23616 0.766040 -0.0161350 2.61401
GHS -0.39773 -0.0075054 -0.12582 -0.016135 0.2047386 0.83022
y -12.67116 -25.1560159 3.50016 2.614013 0.8302206 72.72663
$msg
[1] "0 singular samples of size 7 out of 3000"
$crit
[1] 6.5119
$best
[1] 2 3 4 5 6 7 9 10 11 12 13 16 17 18 20 23 25 27 31 32 35 36 38 41 44
[26] 48 51 52 53 54 55 56 57 60 62
$n.obs
[1] 63
$quan
[1] 35
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
fish 158 6 82 8.859084
Best subsample:
[1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
[20] 20 21 22 23 24 25 26 27 28 32 35 36 37 42 43 44 45 46 47
[39] 48 49 50 51 52 53 54 55 56 57 58 59 60 107 109 110 111 112 113
[58] 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132
[77] 134 135 136 137 138 139
Outliers: 0
------------- *MCD() result: --------------------------
$center
Weight Length1 Length2 Length3 Height Width
348.230 24.800 26.995 30.037 30.954 14.774
$cov
Weight Length1 Length2 Length3 Height Width
Weight 73259.775 1601.93442 1742.15601 2089.13982 1305.5681 -15.32084
Length1 1601.934 38.83231 41.92827 49.17163 25.9685 -0.15279
Length2 1742.156 41.92827 45.35661 53.31114 28.8038 -0.17589
Length3 2089.140 49.17163 53.31114 64.01178 38.9279 -0.86682
Height 1305.568 25.96846 28.80382 38.92787 45.3144 -2.35869
Width -15.321 -0.15279 -0.17589 -0.86682 -2.3587 1.04154
$msg
[1] "0 singular samples of size 7 out of 3000"
$crit
[1] 8.8591
$best
[1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
[20] 20 21 22 23 24 25 26 27 28 32 35 36 37 42 43 44 45 46 47
[39] 48 49 50 51 52 53 54 55 56 57 58 59 60 107 109 110 111 112 113
[58] 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132
[77] 134 135 136 137 138 139
$n.obs
[1] 158
$quan
[1] 82
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
pottery 27 6 17 -10.586933
Best subsample:
[1] 1 2 4 5 6 9 10 11 13 14 15 19 20 21 22 26 27
Outliers: 0
------------- *MCD() result: --------------------------
$center
SI AL FE MG CA TI
54.98333 15.20556 9.70000 3.81667 5.21111 0.85944
$cov
SI AL FE MG CA TI
SI 13.063824 1.451863 -0.0129412 1.349706 -1.143922 0.0559902
AL 1.451863 2.561732 -0.4000000 -1.586569 0.132288 -0.0129379
FE -0.012941 -0.400000 0.1764706 0.338824 -0.222941 0.0090588
MG 1.349706 -1.586569 0.3388235 1.774412 -0.100196 0.0180686
CA -1.143922 0.132288 -0.2229412 -0.100196 0.782222 -0.0219935
TI 0.055990 -0.012938 0.0090588 0.018069 -0.021993 0.0011114
$msg
[1] "0 singular samples of size 7 out of 3000"
$crit
[1] -10.587
$best
[1] 1 2 4 5 6 9 10 11 13 14 15 19 20 21 22 26 27
$n.obs
[1] 27
$quan
[1] 17
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
rice 105 6 56 -14.463986
Best subsample:
[1] 2 4 6 8 10 12 15 18 21 22 24 29 30 31 32 33 34 36 37
[20] 38 41 44 45 47 51 52 53 54 55 59 61 65 67 68 69 70 72 76
[39] 78 79 80 81 82 83 84 85 86 92 93 94 95 97 98 99 102 105
Outliers: 0
------------- *MCD() result: --------------------------
$center
Favor Appearance Taste Stickiness
-0.261143 0.091901 -0.131516 0.074637
Toughness Overall_evaluation
0.068473 -0.209516
$cov
Favor Appearance Taste Stickiness Toughness
Favor 0.37972 0.32416 0.37997 0.37180 -0.18998
Appearance 0.32416 0.54625 0.51414 0.51737 -0.29632
Taste 0.37997 0.51414 0.62865 0.62208 -0.35794
Stickiness 0.37180 0.51737 0.62208 0.79643 -0.46309
Toughness -0.18998 -0.29632 -0.35794 -0.46309 0.42723
Overall_evaluation 0.45786 0.59799 0.71700 0.77311 -0.44109
Overall_evaluation
Favor 0.45786
Appearance 0.59799
Taste 0.71700
Stickiness 0.77311
Toughness -0.44109
Overall_evaluation 0.88794
$msg
[1] "0 singular samples of size 7 out of 3000"
$crit
[1] -14.464
$best
[1] 2 4 6 8 10 12 15 18 21 22 24 29 30 31 32 33 34 36 37
[20] 38 41 44 45 47 51 52 53 54 55 59 61 65 67 68 69 70 72 76
[39] 78 79 80 81 82 83 84 85 86 92 93 94 95 97 98 99 102 105
$n.obs
[1] 105
$quan
[1] 56
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
un86 73 7 40 16.891076
Best subsample:
[1] 9 10 12 14 16 17 18 20 23 24 26 27 31 32 33 37 39 41 42 45 47 48 49 50 51
[26] 52 55 56 57 60 61 62 63 64 65 67 70 71 72 73
Outliers: 0
------------- *MCD() result: --------------------------
$center
POP MOR CAR DR GNP DEN TB
22.52457 68.52174 7.12370 0.90130 1.24739 59.68239 0.44217
$cov
POP MOR CAR DR GNP DEN TB
POP 770.25647 229.95690 -14.63580 -2.645204 -6.6936678 18.7093 0.6785543
MOR 229.95690 2101.32174 -275.88086 -31.396696 -36.6697198 -653.4731 -0.8918261
CAR -14.63580 -275.88086 65.63702 6.005357 9.2014676 90.1669 0.2285518
DR -2.64520 -31.39670 6.00536 0.849207 0.7307013 17.1491 0.0130815
GNP -6.69367 -36.66972 9.20147 0.730701 2.0202730 14.0366 0.0030325
DEN 18.70930 -653.47305 90.16686 17.149066 14.0366419 2208.4689 -1.1267831
TB 0.67855 -0.89183 0.22855 0.013082 0.0030325 -1.1268 0.0158174
$msg
[1] "0 singular samples of size 8 out of 3000"
$crit
[1] 16.891
$best
[1] 9 10 12 14 16 17 18 20 23 24 26 27 31 32 33 37 39 41 42 45 47 48 49 50 51
[26] 52 55 56 57 60 61 62 63 64 65 67 70 71 72 73
$n.obs
[1] 73
$quan
[1] 40
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
wages 36 9 23 25.139287
Best subsample:
[1] 1 2 3 6 7 8 10 11 14 17 20 21 22 23 25 26 27 29 31 33 34 35 36
Outliers: 0
------------- *MCD() result: --------------------------
$center
HRS RATE ERSP ERNO NEIN ASSET AGE DEP
2144.5652 2.8484 1115.4348 303.0870 340.9565 6491.8261 39.4000 2.4663
SCHOOL
10.0913
$cov
HRS RATE ERSP ERNO NEIN ASSET
HRS 3.1775e+03 12.703652 -3.0743e+03 -675.5968 5390.0711 121911.56
RATE 1.2704e+01 0.136870 4.0405e+00 -1.8722 34.5884 805.56
ERSP -3.0743e+03 4.040484 1.0453e+04 165.3696 -3044.3439 -58968.01
ERNO -6.7560e+02 -1.872176 1.6537e+02 1062.9921 -840.3142 -20437.21
NEIN 5.3901e+03 34.588383 -3.0443e+03 -840.3142 12176.3162 273686.95
ASSET 1.2191e+05 805.557943 -5.8968e+04 -20437.2115 273686.9466 6197644.24
AGE -3.9518e+01 -0.177027 3.3995e+01 8.4773 -61.5682 -1451.17
DEP -5.6454e-01 -0.035799 -1.1652e+01 1.6422 -8.4696 -184.88
SCHOOL 3.9405e+01 0.325095 9.9032e-01 -7.9219 90.6542 2110.15
AGE DEP SCHOOL
HRS -3.9518e+01 -0.564543 39.405138
RATE -1.7703e-01 -0.035799 0.325095
ERSP 3.3995e+01 -11.651729 0.990316
ERNO 8.4773e+00 1.642154 -7.921937
NEIN -6.1568e+01 -8.469623 90.654150
ASSET -1.4512e+03 -184.879808 2110.152964
AGE 7.4818e-01 -0.042855 -0.569545
DEP -4.2855e-02 0.051342 -0.073393
SCHOOL -5.6955e-01 -0.073393 0.840830
$msg
[1] "0 singular samples of size 10 out of 3000"
$crit
[1] 25.139
$best
[1] 1 2 3 6 7 8 10 11 14 17 20 21 22 23 25 26 27 29 31 33 34 35 36
$n.obs
[1] 36
$quan
[1] 23
--------------------------------------------------------
========================================================
>
> ###--- now the "close to singular" mahalanobis case:
> set.seed(6)
> (c3 <- covMcd(mort3))
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=34); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = mort3)
Log(Det.): 37.5
Robust Estimate of Location:
MO70 MAGE CI68 MDOC DENS NONW EDUC IN69
113.06 287.91 164.84 155.76 19.56 2.23 558.23 106.91
Robust Estimate of Covariance:
MO70 MAGE CI68 MDOC DENS NONW EDUC IN69
MO70 540.1 497.3190 62.46 107.37 -20.17 10.6107 -766.8 -107.88
MAGE 497.3 747.7620 4.57 222.17 -75.53 -0.0169 -443.7 3.43
CI68 62.5 4.5663 588.93 -253.26 -65.58 5.1532 -659.0 19.76
MDOC 107.4 222.1690 -253.26 1629.27 -28.72 1.9300 296.0 100.86
DENS -20.2 -75.5255 -65.58 -28.72 124.97 8.2075 -325.0 -42.70
NONW 10.6 -0.0169 5.15 1.93 8.21 2.1620 -85.5 -7.87
EDUC -766.8 -443.7455 -659.00 295.96 -324.95 -85.4782 5850.0 446.59
IN69 -107.9 3.4259 19.76 100.86 -42.70 -7.8714 446.6 111.20
> (c3. <- covMcd(mort3, nsamp="deterministic"))
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=34)
Call:
covMcd(x = mort3, nsamp = "deterministic")
iBest: 2; C-step iterations: 3, 3, 3, 2, 2, 3
Log(Det.): 38
Robust Estimate of Location:
MO70 MAGE CI68 MDOC DENS NONW EDUC IN69
111.41 286.52 164.44 155.62 19.50 2.24 556.46 107.68
Robust Estimate of Covariance:
MO70 MAGE CI68 MDOC DENS NONW EDUC IN69
MO70 599.72 511.165 84.86 128.44 -5.08 14.133 -643 -113.52
MAGE 511.16 736.618 12.89 184.81 -78.70 0.249 -353 12.26
CI68 84.86 12.891 630.10 -235.70 -58.52 4.483 -657 37.68
MDOC 128.44 184.814 -235.70 1520.48 11.12 6.648 287 61.60
DENS -5.08 -78.700 -58.52 11.12 134.09 9.919 -282 -50.87
NONW 14.13 0.249 4.48 6.65 9.92 2.407 -75 -8.91
EDUC -643.45 -352.533 -657.02 286.66 -282.25 -75.004 5333 375.55
IN69 -113.52 12.257 37.68 61.60 -50.87 -8.912 376 136.08
> stopifnot(log(c3$crit) <= log(c3.$crit),
+ print(log(c3.$crit / c3$crit)) <= 0.8)
[1] 0.013676
> ## see 0.516 / 0.291 {with seed 7}
> ##
> ## rescale variables:
> scaleV <- c(0.1, 0.1, 1, 1, .001, 0.1, 0.1, 100)
> mm <- data.matrix(mort3) * rep(scaleV, each = nrow(mort3))
> C3 <- covMcd(mm)
> C3. <- covMcd(mm, nsamp="deterministic")
> stopifnot(C3$mcd.wt == c3$mcd.wt)# here, not for all seeds!
>
> ## error ("computationally singular") with old (too high) default tolerance:
> try( covMcd(mm, control= rrcov.control(tol = 1e-10)) )
Error in solve.default(cov, ...) :
system is computationally singular: reciprocal condition number = 2.4435e-11
> try( covMcd(mm, control= rrcov.control(tol = 1e-10), nsamp="deterministic") )
Error in solve.default(cov, ...) :
system is computationally singular: reciprocal condition number = 2.71945e-11
>
> showProc.time()
Time (user system elapsed): 3.14 0.41 3.59
>
> ## "large" examples using different algo branches {seg.fault in version 0.4-4}:
>
> n <- 600 ## - partitioning will be triggered
> set.seed(1)
> X <- matrix(round(100*rnorm(n * 3)), n, 3)
> (cX <- covMcd(X))
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=302); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = X)
Log(Det.): 25.1
Robust Estimate of Location:
[1] 0.141 -6.083 -0.703
Robust Estimate of Covariance:
[,1] [,2] [,3]
[1,] 9321 -111 376
[2,] -111 10842 242
[3,] 376 242 11330
> cX. <- covMcd(X, nsamp="deterministic", scalefn = scaleTau2)
> i <- names(cX); i <- i[!(i %in% c("call", "nsamp", "method", "raw.weights"))]
> stopifnot(sum(cX.$raw.weights != cX$raw.weights) <= 2,
+ all.equal(cX[i], cX.[i], tol= 1/9))
>
> n <- 2000 ## - nesting will be triggered
> set.seed(4)
> X <- matrix(round(100*rnorm(n * 3)), n, 3)
> set.seed(1)
> summary(cX <- covMcd(X)) # <- show newly activated print.summary.mcd(.)
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=1002); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = X)
Log(Det.): 24.9
Robust Estimate of Location:
[1] 0.422 -0.422 -0.252
Robust Estimate of Covariance:
[,1] [,2] [,3]
[1,] 9861.1 -60.6 74
[2,] -60.6 9472.4 -273
[3,] 74.0 -273.0 10034
Eigenvalues:
[1] 10172 9836 9360
Robust Distances:
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0171 1.1700 2.4300 3.0100 4.1400 15.8000
Robustness weights:
52 observations c(118,122,130,152,155,159,181,246,266,376,394,432,483,517,608,666,730,774,792,840,913,971,986,1067,1095,1099,1106,1129,1167,1179,1222,1261,1276,1293,1412,1443,1499,1534,1570,1573,1589,1596,1622,1633,1712,1714,1726,1784,1795,1805,1845,1891)
are outliers with |weight| = 0 ( < 5e-05);
1948 weights are ~= 1.
> cX. <- covMcd(X, nsamp="deterministic", scalefn = scaleTau2)
> i2 <- i[i != "mcd.wt"]
> stopifnot(print(sum(cX.$raw.weights != cX$raw.weights)) <= 3, # 2
+ all.equal(cX[i2], cX.[i2], tol= 1/10))# 1/16
[1] 2
>
> set.seed(1) ## testing of 'raw.only' :
> cXo <- covMcd(X, raw.only=TRUE)
> i <- paste0("raw.", c("cov", "center", "cnp2"))
> stopifnot(cXo$raw.only, all.equal(cX[i], cXo[i], tol = 1e-15),
+ c("best", "mah") %in% setdiff(names(cX), names(cXo)))
> showProc.time()
Time (user system elapsed): 0.33 0.02 0.35
>
> ## Now, some small sample cases:
>
> ## maximal values:
> n. <- 10
> p. <- 8
> set.seed(44)
> (X. <- cbind(1:n., round(10*rt(n.,3)), round(10*rt(n.,2)),
+ matrix(round(10*rnorm(n. * (p.-3)), 1), nrow = n., ncol = p.-3)))
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 1 8 0 -3.6 4.7 3.0 -7.7 -3.3
[2,] 2 -24 3 5.7 -15.6 13.5 -8.9 -10.0
[3,] 3 -1 0 17.0 -1.9 19.0 17.4 -5.8
[4,] 4 -9 2 0.1 -6.0 -11.5 18.6 25.8
[5,] 5 -6 -31 2.4 10.0 9.6 5.4 -4.8
[6,] 6 6 -3 -12.3 -4.6 17.2 -4.6 15.2
[7,] 7 22 16 -2.8 -2.2 -5.2 -2.2 5.6
[8,] 8 23 5 -9.0 -10.4 -2.6 -5.7 2.0
[9,] 9 1 -9 2.1 -5.6 4.1 2.8 -3.0
[10,] 10 -17 -2 -8.8 -7.8 6.5 4.2 17.7
>
> ## 2 x 1 ---> Error
> r <- tryCatch(covMcd(X.[1:2, 2, drop=FALSE]), error=function(e)e)
> stopifnot(inherits(r, "error"),
+ grepl("too small sample size", r$message))
>
> ## 3 x 2 --- ditto
> r <- tryCatch(covMcd(X.[1:3, 2:3]), error=function(e)e)
> stopifnot(inherits(r, "error"),
+ grepl("too small sample size", r$message))
>
> ## 5 x 3 [ n < 2 p ! ] --- also works for MASS
> X <- X.[1:5, 1:3]
> set.seed(101)
> ## the finite-sample correction is definitely doubtful:
> summary(cc <- covMcd(X, use.correction = FALSE))
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=4); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = X, use.correction = FALSE)
Log(Det.): 4.3
Robust Estimate of Location:
[1] 2.50 -6.50 1.25
Robust Estimate of Covariance:
[,1] [,2] [,3]
[1,] 1.797 -5.03 0.539
[2,] -5.033 198.80 -20.671
[3,] 0.539 -20.67 2.427
Eigenvalues:
[1] 201.080 1.669 0.274
Robust Distances:
Min. 1st Qu. Median Mean 3rd Qu. Max.
2.1 2.1 2.1 752.0 2.1 3750.0
Robustness weights:
[1] 1 1 1 1 0
Warning message:
In covMcd(X, use.correction = FALSE) :
n < 2 * p, i.e., possibly too small sample size
> str(cc) ## best = 2 3 4 5
List of 19
$ call : language covMcd(x = X, use.correction = FALSE)
$ nsamp : num 500
$ method : chr "Fast MCD(alpha=0.5 ==> h=4); nsamp = 500; (n,k)mini = (300,5)"
$ cov : num [1:3, 1:3] 1.797 -5.033 0.539 -5.033 198.8 ...
$ center : num [1:3] 2.5 -6.5 1.25
$ n.obs : int 5
$ best : int [1:4] 1 2 3 4
$ alpha : num 0.5
$ quan : num 4
$ raw.cov : num [1:3, 1:3] 2.474 -6.928 0.742 -6.928 273.675 ...
$ raw.center : num [1:3] 2.5 -6.5 1.25
$ raw.weights: num [1:5] 1 1 1 1 0
$ crit : num 4.3
$ raw.mah : num [1:5] 1.52 1.52 1.52 1.52 2724.44
$ mah : num [1:5] 2.09 2.09 2.09 2.09 3750.56
$ mcd.wt : num [1:5] 1 1 1 1 0
$ X : num [1:5, 1:3] 1 2 3 4 5 8 -24 -1 -9 -6 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:5] "1" "2" "3" "4" ...
.. ..$ : NULL
$ raw.cnp2 : num [1:2] 1.48 1
$ cnp2 : num [1:2] 1.08 1
- attr(*, "class")= chr "mcd"
> if(hasMASS <- requireNamespace("MASS", quietly=TRUE)) {
+ mcc <- MASS::cov.mcd(X)
+ stopifnot(cc$best == mcc$best,
+ all.equal(cc$center, mcc$center, tolerance = 1e-10),
+ all.equal(c(mcc$cov / cc$raw.cov), rep(0.673549282206, 3*3)))
+ }
> ## p = 4 -- 6 x 4 & 7 x 4 [ n < 2 p ! ]
> p <- 4
> n <- 7
> X <- X.[1:n, 1+(1:p)]
> stopifnot(dim(X) == c(n,p))
> (cc <- covMcd(X, use.correction = FALSE))
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=6); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = X, use.correction = FALSE)
Log(Det.): 15.6
Robust Estimate of Location:
[1] 0.333 3.000 0.683 -4.267
Robust Estimate of Covariance:
[,1] [,2] [,3] [,4]
[1,] 264.3 50.669 -68.183 85.250
[2,] 50.7 47.688 -0.617 -0.724
[3,] -68.2 -0.617 104.485 -12.456
[4,] 85.2 -0.724 -12.456 47.227
Warning message:
In covMcd(X, use.correction = FALSE) :
n < 2 * p, i.e., possibly too small sample size
> str(cc) ## best = 1 2 4 5 6 7
List of 19
$ call : language covMcd(x = X, use.correction = FALSE)
$ nsamp : num 500
$ method : chr "Fast MCD(alpha=0.5 ==> h=6); nsamp = 500; (n,k)mini = (300,5)"
$ cov : num [1:4, 1:4] 264.3 50.7 -68.2 85.2 50.7 ...
$ center : num [1:4] 0.333 3 0.683 -4.267
$ n.obs : int 7
$ best : int [1:6] 1 2 3 4 6 7
$ alpha : num 0.5
$ quan : num 6
$ raw.cov : num [1:4, 1:4] 319 61.2 -82.3 102.9 61.2 ...
$ raw.center : num [1:4] 0.333 3 0.683 -4.267
$ raw.weights: num [1:7] 1 1 1 1 0 1 1
$ crit : num 15.6
$ raw.mah : num [1:7] 2.546 2.477 3.224 0.835 24.765 ...
$ mah : num [1:7] 3.07 2.99 3.89 1.01 29.89 ...
$ mcd.wt : num [1:7] 1 1 1 1 0 1 1
$ X : num [1:7, 1:4] 8 -24 -1 -9 -6 6 22 0 3 0 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:7] "1" "2" "3" "4" ...
.. ..$ : NULL
$ raw.cnp2 : num [1:2] 1.28 1
$ cnp2 : num [1:2] 1.06 1
- attr(*, "class")= chr "mcd"
> if(hasMASS) {
+ mcc <- MASS::cov.mcd(X)
+ stopifnot(cc$best == mcc$best,
+ all.equal(cc$center, mcc$center, tolerance = 1e-10),
+ all.equal(c(mcc$cov / cc$raw.cov), rep(0.7782486992881, p*p)))
+ }
>
> n <- 6
> X <- X[1:n,]
> (cc <- covMcd(X, use.correction = FALSE))
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=5); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = X, use.correction = FALSE)
Log(Det.): 7.67
Robust Estimate of Location:
[1] -4.00 0.40 1.38 -4.68
Robust Estimate of Covariance:
[,1] [,2] [,3] [,4]
[1,] 180.4 -26.61 -61.1 92.26
[2,] -26.6 5.64 13.7 -9.48
[3,] -61.1 13.69 126.7 -13.27
[4,] 92.3 -9.48 -13.3 57.67
Warning message:
In covMcd(X, use.correction = FALSE) :
n < 2 * p, i.e., possibly too small sample size
> if(hasMASS) {
+ mcc <- MASS::cov.mcd(X)
+ stopifnot(cc$best == mcc$best,
+ all.equal(cc$center, mcc$center, tolerance = 1e-10),
+ all.equal(c(mcc$cov / cc$raw.cov), rep(0.7528695976179, p*p)))
+ }
>
> showProc.time()
Time (user system elapsed): 0.03 0 0.03
>
> ## nsamp = "exact" -- here for p=7
> coleman.x <- data.matrix(coleman[, 1:6])
> showSys.time(CcX <- covMcd(coleman.x, nsamp= "exact"))
Time user system elapsed
Time 0.70 0.00 0.71
> showSys.time(Ccd <- covMcd(coleman.x, nsamp= "deterministic"))
Time user system elapsed
Time 0.02 0.00 0.01
> stopifnot(all.equal(CcX$best,
+ c(2, 5:9, 11,13, 14:16, 19:20), tolerance=0),
+ intersect(CcX$best, Ccd$best) == c(2,5,7,8,13,14,16,19,20),
+ relErr(CcX$crit, Ccd$crit) < 0.35 # see ~ 0.34
+ )
> summary(Ccd)
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Deterministic MCD(alpha=0.5 ==> h=13)
Call:
covMcd(x = coleman.x, nsamp = "deterministic")
iBest: 1; C-step iterations: 3, 2, 2, 2, 2, 2
Log(Det.): 1.85
Robust Estimate of Location:
salaryP fatherWc sstatus teacherSc motherLev Y
2.76 48.38 6.12 25.00 6.40 36.53
Robust Estimate of Covariance:
salaryP fatherWc sstatus teacherSc motherLev Y
salaryP 0.3367 2.37 -0.354 0.201 0.0997 -0.863
fatherWc 2.3742 1732.58 439.328 16.754 45.8650 254.718
sstatus -0.3541 439.33 159.367 5.095 13.4665 90.241
teacherSc 0.2013 16.75 5.095 1.044 0.7381 2.075
motherLev 0.0997 45.86 13.466 0.738 1.3859 7.403
Y -0.8630 254.72 90.241 2.075 7.4030 57.565
Eigenvalues:
[1] 1.89e+03 5.81e+01 5.10e+00 8.07e-01 2.16e-01 1.93e-02
Robust Distances:
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.859 1.920 2.850 15.100 21.500 71.900
Robustness weights:
7 observations c(1,6,9,10,11,15,18) are outliers with |weight| = 0 ( < 0.005);
13 weights are ~= 1.
>
>
> demo(determinMCD)## ../demo/determinMCD.R
demo(determinMCD)
---- ~~~~~~~~~~~
> library(robustbase)
> source(system.file("xtraR/test_MCD.R", package = "robustbase"))#-> doMCDdata()
> ##' This version of domcd() runs *both* "Fast" and "deterministic" MCD
> ##' @title covMcd() "workhorse" function -- *passed* to and from doMCDdata()
> ##' @param x data set: n x p numeric matrix
> ##' @param xname "promise" which will be substituted() and printed
> ##' @param nrep number of repetition: only sensible for *timing*
> ##' @param time
> ##' @param short
> ##' @param full
> ##' @param lname optional:
> ##' @param seed optional:
> ##' @param trace optional:
> domcd.2 <- function(x, xname, nrep=1,
+ do.exact = NULL, # <- smart default, globally customizable
+ time = get("time", parent.frame()), # compromise
+ short = get("short", parent.frame()), # compromise
+ full = get("full", parent.frame()), # compromise
+ lname=20, seed=123, trace=FALSE)
+ {
+ if(short && full)
+ stop("you should not set both 'full' and 'short' to TRUE")
+ force(xname)# => evaluate when it is a data(<>, ..) call
+ n <- dim(x)[1]
+ p <- dim(x)[2]
+ metha <- "FastMCD"
+ methb <- "detMCD"
+ if(is.null(do.exact)) {
+ nLarge <- if(exists("nLarge", mode="numeric"))
+ get("nLarge", mode="numeric") else 5000
+ do.exact <- choose(n, p+1L) < nLarge
+ }
+ set.seed(seed); mcda <- covMcd(x, trace=trace)
+ set.seed(seed); mcdb <- covMcd(x, nsamp="deterministic", trace=trace)
+ if(do.exact) {
+ methX <- "exactMCD"
+ set.seed(seed); mcdX <- covMcd(x, nsamp="exact", trace=trace)
+ }
+ mkRes <- function(mcd)
+ sprintf("%3d %3d %3d %12.6f\n", n,p, mcd$quan, mcd$crit)
+ xresa <- mkRes(mcda)
+ xresb <- mkRes(mcdb)
+ if(do.exact) xresX <- mkRes(mcdX)
+ if(time) {
+ tim1 <- function(meth)
+ sprintf("%10.3f\n", system.time(repMCD(x, nrep, meth))[1]/nrep)
+ xresa <- paste(xresa, tim1(metha))
+ xresb <- paste(xresb, tim1(methb))
+ if(do.exact) xresX <- paste(xresX, tim1(methX))
+ }
+ if(full) {
+ header <- get("header", parent.frame())
+ header(time)
+ }
+ ## lname: must fit to header():
+ x.meth <- paste(xname, format(c(metha, methb, if(do.exact) methX)))
+ cat(sprintf("%*s", lname, x.meth[1]), xresa)
+ cat(sprintf("%*s", lname, x.meth[2]), xresb)
+ if(do.exact) cat(sprintf("%*s", lname, x.meth[3]), xresX)
+ cat("Best subsamples: \n")
+ cat(sprintf(" %10s: ", metha)); print(mcda$best)
+ if(identical(mcdb$best, mcda$best))
+ cat(sprintf(" %s is the same as %s\n", methb, metha))
+ else {
+ cat(sprintf(" %10s: ", methb)); print(mcdb$best)
+ cat(sprintf(" Difference %s - %s:", methb, metha))
+ print(setdiff(mcdb$best, mcda$best))
+ }
+ if(do.exact) {
+ if(identical(mcda$best, mcdX$best))
+ cat(sprintf(" %s is the same as %s\n", methX, metha))
+ else if(identical(mcdb$best, mcdX$best))
+ cat(sprintf(" %s is the same as %s\n", methX, methb))
+ else {
+ cat(sprintf(" %10s: ", methX)); print(mcdX$best)
+ }
+ }
+ if(!short) {
+ cat("Details about", metha,": ")
+ ibad <- which(mcda$wt==0)
+ names(ibad) <- NULL
+ nbad <- length(ibad)
+ cat("Outliers: ",nbad,"\n")
+ if(nbad > 0)
+ print(ibad)
+ if(full){
+ cat("-------------\n")
+ print(mcda)
+ }
+ cat("--------------------------------------------------------\n")
+ }
+ }
> doMCDdata(domcd = domcd.2)
Call: doMCDdata(domcd = domcd.2)
Data Set n p h(alf) LOG(obj)
=============================================
bushfire FastMCD 38 5 22 18.135810
bushfire detMCD 38 5 22 18.135810
Best subsamples:
FastMCD: [1] 1 2 3 4 5 6 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
detMCD is the same as FastMCD
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=22); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): 18.1
Robust Estimate of Location:
V1 V2 V3 V4 V5
105 147 274 218 279
Robust Estimate of Covariance:
V1 V2 V3 V4 V5
V1 346 268 -1692 -381 -311
V2 268 236 -1125 -230 -194
V3 -1692 -1125 9993 2455 1951
V4 -381 -230 2455 647 505
V5 -311 -194 1951 505 398
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
heart FastMCD 12 2 7 5.678742
heart detMCD 12 2 7 5.678742
heart exactMCD 12 2 7 5.678742
Best subsamples:
FastMCD: [1] 1 3 4 5 7 9 11
detMCD is the same as FastMCD
exactMCD is the same as FastMCD
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=7); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): 5.68
Robust Estimate of Location:
height weight
38.3 33.1
Robust Estimate of Covariance:
height weight
height 135 259
weight 259 564
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
starsCYG FastMCD 47 2 25 -8.031215
starsCYG detMCD 47 2 25 -8.028718
Best subsamples:
FastMCD: [1] 1 2 4 6 8 10 12 13 16 24 25 26 28 32 33 37 38 39 40 41 42 43 44 45 46
detMCD: [1] 1 6 10 12 13 16 23 24 25 26 28 31 32 33 37 38 39 40 41 42 43 44 45 46 47
Difference detMCD - FastMCD:[1] 23 31 47
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=25); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): -8.03
Robust Estimate of Location:
log.Te log.light
4.41 4.95
Robust Estimate of Covariance:
log.Te log.light
log.Te 0.0132 0.0394
log.light 0.0394 0.2743
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
stackloss FastMCD 21 3 12 5.472581
stackloss detMCD 21 3 12 6.577286
Best subsamples:
FastMCD: [1] 4 5 6 7 8 9 10 11 12 13 14 20
detMCD: [1] 4 5 6 7 8 9 11 13 16 18 19 20
Difference detMCD - FastMCD:[1] 16 18 19
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=12); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): 5.47
Robust Estimate of Location:
Air.Flow Water.Temp Acid.Conc.
59.5 20.8 87.3
Robust Estimate of Covariance:
Air.Flow Water.Temp Acid.Conc.
Air.Flow 6.29 5.85 5.74
Water.Temp 5.85 9.23 6.14
Acid.Conc. 5.74 6.14 23.25
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
phosphor FastMCD 18 2 10 6.878847
phosphor detMCD 18 2 10 7.732906
phosphor exactMCD 18 2 10 6.878847
Best subsamples:
FastMCD: [1] 3 5 8 9 11 12 13 14 15 17
detMCD: [1] 2 4 5 7 8 9 11 12 14 16
Difference detMCD - FastMCD:[1] 2 4 7 16
exactMCD is the same as FastMCD
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=10); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): 6.88
Robust Estimate of Location:
inorg organic
13.4 38.8
Robust Estimate of Covariance:
inorg organic
inorg 129 130
organic 130 182
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
coleman FastMCD 20 5 13 1.286808
coleman detMCD 20 5 13 2.149184
Best subsamples:
FastMCD: [1] 2 3 4 5 7 8 12 13 14 16 17 19 20
detMCD: [1] 3 4 5 7 8 12 13 14 16 17 18 19 20
Difference detMCD - FastMCD:[1] 18
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=13); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): 1.29
Robust Estimate of Location:
salaryP fatherWc sstatus teacherSc motherLev
2.76 48.38 6.12 25.00 6.40
Robust Estimate of Covariance:
salaryP fatherWc sstatus teacherSc motherLev
salaryP 0.253 1.79 -0.266 0.151 0.075
fatherWc 1.786 1303.38 330.496 12.604 34.503
sstatus -0.266 330.50 119.888 3.833 10.131
teacherSc 0.151 12.60 3.833 0.785 0.555
motherLev 0.075 34.50 10.131 0.555 1.043
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
salinity FastMCD 28 3 16 1.326364
salinity detMCD 28 3 16 1.940763
Best subsamples:
FastMCD: [1] 1 2 6 7 8 12 13 14 18 20 21 22 25 26 27 28
detMCD: [1] 1 8 10 12 13 14 15 17 18 20 21 22 25 26 27 28
Difference detMCD - FastMCD:[1] 10 15 17
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=16); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): 1.33
Robust Estimate of Location:
X1 X2 X3
10.08 2.78 22.78
Robust Estimate of Covariance:
X1 X2 X3
X1 10.44 1.01 -3.19
X2 1.01 3.83 -1.44
X3 -3.19 -1.44 2.39
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
wood FastMCD 20 5 13 -36.270094
wood detMCD 20 5 13 -35.240819
Best subsamples:
FastMCD: [1] 1 2 3 5 9 10 12 13 14 15 17 18 20
detMCD: [1] 1 2 3 5 9 11 12 13 14 15 17 18 20
Difference detMCD - FastMCD:[1] 11
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=13); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): -36.3
Robust Estimate of Location:
x1 x2 x3 x4 x5
0.587 0.122 0.531 0.538 0.892
Robust Estimate of Covariance:
x1 x2 x3 x4 x5
x1 0.010025 1.88e-03 0.003153 -0.000586 -1.63e-03
x2 0.001881 4.85e-04 0.001269 -0.000052 2.36e-05
x3 0.003153 1.27e-03 0.006632 -0.000871 3.52e-04
x4 -0.000586 -5.20e-05 -0.000871 0.002846 1.83e-03
x5 -0.001630 2.36e-05 0.000352 0.001828 2.77e-03
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
hbk FastMCD 75 3 39 -1.047858
hbk detMCD 75 3 39 -1.045501
Best subsamples:
FastMCD: [1] 15 16 17 18 19 20 21 22 23 24 26 27 31 32 33 35 36 37 38 40 43 49 50 51 54
[26] 55 56 58 59 61 63 64 66 67 70 71 72 73 74
detMCD: [1] 15 17 18 19 20 21 22 23 24 26 27 28 29 32 33 35 36 38 40 41 43 48 49 50 51
[26] 54 55 56 58 59 63 64 66 67 70 71 72 73 74
Difference detMCD - FastMCD:[1] 28 29 41 48
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=39); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): -1.05
Robust Estimate of Location:
X1 X2 X3
1.54 1.78 1.69
Robust Estimate of Covariance:
X1 X2 X3
X1 1.227 0.055 0.127
X2 0.055 1.249 0.153
X3 0.127 0.153 1.160
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
Animals FastMCD 28 2 15 14.555543
Animals detMCD 28 2 15 14.555543
Animals exactMCD 28 2 15 14.555543
Best subsamples:
FastMCD: [1] 1 3 4 5 10 11 17 18 19 20 21 22 23 26 27
detMCD is the same as FastMCD
exactMCD is the same as FastMCD
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=15); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): 14.6
Robust Estimate of Location:
body brain
18.7 64.9
Robust Estimate of Covariance:
body brain
body 929 1576
brain 1576 5646
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
milk FastMCD 86 8 47 -28.931843
milk detMCD 86 8 47 -28.844954
Best subsamples:
FastMCD: [1] 5 7 8 9 10 22 23 24 26 30 31 32 33 34 35 37 38 39 45 46 49 51 53 54 55
[26] 56 57 58 59 60 61 63 64 65 66 67 68 69 71 72 76 78 79 81 83 84 86
detMCD: [1] 5 8 9 10 21 22 23 24 26 30 31 32 33 34 35 36 37 38 39 46 51 53 54 55 56
[26] 57 58 59 60 61 62 63 64 65 66 67 68 69 71 72 76 78 79 81 83 84 86
Difference detMCD - FastMCD:[1] 21 36 62
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=47); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): -28.9
Robust Estimate of Location:
X1 X2 X3 X4 X5 X6 X7 X8
1.03 35.76 33.05 26.12 25.10 25.04 122.94 14.36
Robust Estimate of Covariance:
X1 X2 X3 X4 X5 X6 X7
X1 4.68e-07 8.92e-05 0.00018 0.000172 0.000152 0.000143 0.000625
X2 8.92e-05 1.56e+00 0.21893 0.161497 0.101095 0.197334 1.278580
X3 1.80e-04 2.19e-01 1.17765 0.868701 0.855642 0.864872 0.690044
X4 1.72e-04 1.61e-01 0.86870 0.688578 0.659177 0.660833 0.565031
X5 1.52e-04 1.01e-01 0.85564 0.659177 0.692458 0.667944 0.570607
X6 1.43e-04 1.97e-01 0.86487 0.660833 0.667944 0.693997 0.572373
X7 6.25e-04 1.28e+00 0.69004 0.565031 0.570607 0.572373 3.468208
X8 3.52e-06 1.15e-01 0.17236 0.114700 0.097445 0.107939 0.211966
X8
X1 3.52e-06
X2 1.15e-01
X3 1.72e-01
X4 1.15e-01
X5 9.74e-02
X6 1.08e-01
X7 2.12e-01
X8 1.16e-01
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
lactic FastMCD 20 2 11 0.359580
lactic detMCD 20 2 11 0.359580
lactic exactMCD 20 2 11 0.359580
Best subsamples:
FastMCD: [1] 1 2 3 4 5 7 8 9 10 11 12
detMCD is the same as FastMCD
exactMCD is the same as FastMCD
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=11); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): 0.36
Robust Estimate of Location:
X Y
3.86 5.01
Robust Estimate of Covariance:
X Y
X 10.6 14.6
Y 14.6 21.3
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
pension FastMCD 18 2 10 16.675508
pension detMCD 18 2 10 16.675508
pension exactMCD 18 2 10 16.675508
Best subsamples:
FastMCD: [1] 1 2 3 4 5 6 8 9 11 12
detMCD is the same as FastMCD
exactMCD is the same as FastMCD
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=10); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): 16.7
Robust Estimate of Location:
Income Reserves
52.3 560.9
Robust Estimate of Covariance:
Income Reserves
Income 1420 11932
Reserves 11932 208643
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
pilot FastMCD 20 2 11 6.487287
pilot detMCD 20 2 11 7.023173
pilot exactMCD 20 2 11 6.487287
Best subsamples:
FastMCD: [1] 2 3 6 7 9 12 15 16 17 18 20
detMCD: [1] 1 2 3 4 8 11 12 13 14 15 19
Difference detMCD - FastMCD:[1] 1 4 8 11 13 14 19
exactMCD is the same as FastMCD
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=11); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): 6.49
Robust Estimate of Location:
X Y
101.1 67.7
Robust Estimate of Covariance:
X Y
X 3344 1070
Y 1070 343
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
vaso FastMCD 39 2 21 -3.972244
vaso detMCD 39 2 21 -3.972244
Best subsamples:
FastMCD: [1] 3 4 8 14 18 19 20 21 22 23 24 25 26 27 28 33 34 35 37 38 39
detMCD is the same as FastMCD
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=21); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): -3.97
Robust Estimate of Location:
Volume Rate
1.16 1.72
Robust Estimate of Covariance:
Volume Rate
Volume 0.313 -0.167
Rate -0.167 0.728
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
wagnerGrowth FastMCD 63 6 35 6.610368
wagnerGrowth detMCD 63 6 35 6.511864
Best subsamples:
FastMCD: [1] 2 3 4 5 6 7 9 10 11 12 13 16 18 20 23 25 26 27 31 32 35 36 38 41 44
[26] 48 51 52 53 54 55 56 57 60 62
detMCD: [1] 2 3 4 5 6 7 9 10 11 12 13 16 17 18 20 23 25 27 31 32 35 36 38 41 44
[26] 48 51 52 53 54 55 56 57 60 62
Difference detMCD - FastMCD:[1] 17
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=35); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): 6.61
Robust Estimate of Location:
Region PA GPA HS GHS y
10.872 33.408 -1.919 2.461 0.369 7.879
Robust Estimate of Covariance:
Region PA GPA HS GHS y
Region 35.3392 15.3047 0.0232 -0.55317 -0.35789 -8.77
PA 15.3047 21.7332 -3.7447 -0.73355 0.09486 -24.54
GPA 0.0232 -3.7447 5.1610 0.23781 -0.14571 5.34
HS -0.5532 -0.7336 0.2378 0.68319 0.00711 2.02
GHS -0.3579 0.0949 -0.1457 0.00711 0.24753 1.40
y -8.7720 -24.5388 5.3353 2.01779 1.39654 78.82
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
fish FastMCD 158 6 82 8.879005
fish detMCD 158 6 82 8.880459
Best subsamples:
FastMCD: [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
[20] 20 21 22 23 24 25 26 27 28 30 32 35 36 37 42 43 44 45 46
[39] 47 48 49 50 51 52 53 54 55 56 57 58 59 60 107 109 110 111 113
[58] 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132
[77] 134 135 136 137 138 139
detMCD: [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
[20] 20 21 22 23 24 25 26 27 35 36 37 42 43 44 45 46 47 48 49
[39] 50 51 52 53 54 55 56 57 58 59 60 106 107 108 109 110 111 112 113
[58] 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132
[77] 134 135 136 137 138 139
Difference detMCD - FastMCD:[1] 106 108 112
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=82); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): 8.88
Robust Estimate of Location:
Weight Length1 Length2 Length3 Height Width
329.9 24.5 26.6 29.7 31.1 14.7
Robust Estimate of Covariance:
Weight Length1 Length2 Length3 Height Width
Weight 69083.0 1477.81 1613.6 1992.62 1439.32 -62.12
Length1 1477.8 34.68 37.6 45.51 28.82 -1.31
Length2 1613.6 37.61 40.9 49.52 31.81 -1.40
Length3 1992.6 45.51 49.5 61.16 42.65 -2.25
Height 1439.3 28.82 31.8 42.65 46.74 -2.82
Width -62.1 -1.31 -1.4 -2.25 -2.82 1.01
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
pottery FastMCD 27 6 17 -10.586933
pottery detMCD 27 6 17 -10.586933
Best subsamples:
FastMCD: [1] 1 2 4 5 6 9 10 11 13 14 15 19 20 21 22 26 27
detMCD is the same as FastMCD
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=17); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): -10.6
Robust Estimate of Location:
SI AL FE MG CA TI
54.983 15.206 9.700 3.817 5.211 0.859
Robust Estimate of Covariance:
SI AL FE MG CA TI
SI 20.5823 2.2874 -0.0204 2.1265 -1.8023 0.08821
AL 2.2874 4.0361 -0.6302 -2.4997 0.2084 -0.02038
FE -0.0204 -0.6302 0.2780 0.5338 -0.3512 0.01427
MG 2.1265 -2.4997 0.5338 2.7956 -0.1579 0.02847
CA -1.8023 0.2084 -0.3512 -0.1579 1.2324 -0.03465
TI 0.0882 -0.0204 0.0143 0.0285 -0.0347 0.00175
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
rice FastMCD 105 6 56 -14.463986
rice detMCD 105 6 56 -14.423048
Best subsamples:
FastMCD: [1] 2 4 6 8 10 12 15 18 21 22 24 29 30 31 32 33 34 36 37
[20] 38 41 44 45 47 51 52 53 54 55 59 61 65 67 68 69 70 72 76
[39] 78 79 80 81 82 83 84 85 86 92 93 94 95 97 98 99 102 105
detMCD: [1] 4 6 8 10 13 15 16 17 18 25 27 29 30 31 32 33 34 36 37
[20] 38 44 45 47 51 52 53 55 59 60 65 66 67 70 72 74 76 78 79
[39] 80 81 82 83 84 85 86 90 92 93 94 95 97 98 99 100 101 105
Difference detMCD - FastMCD: [1] 13 16 17 25 27 60 66 74 90 100 101
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=56); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): -14.5
Robust Estimate of Location:
Favor Appearance Taste Stickiness
-0.2731 0.0600 -0.1468 0.0646
Toughness Overall_evaluation
0.0894 -0.2192
Robust Estimate of Covariance:
Favor Appearance Taste Stickiness Toughness
Favor 0.388 0.323 0.393 0.389 -0.195
Appearance 0.323 0.503 0.494 0.494 -0.270
Taste 0.393 0.494 0.640 0.629 -0.361
Stickiness 0.389 0.494 0.629 0.815 -0.486
Toughness -0.195 -0.270 -0.361 -0.486 0.451
Overall_evaluation 0.471 0.575 0.723 0.772 -0.457
Overall_evaluation
Favor 0.471
Appearance 0.575
Taste 0.723
Stickiness 0.772
Toughness -0.457
Overall_evaluation 0.882
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
un86 FastMCD 73 7 40 16.891076
un86 detMCD 73 7 40 17.117142
Best subsamples:
FastMCD: [1] 9 10 12 14 16 17 18 20 23 24 26 27 31 32 33 37 39 41 42 45 47 48 49 50 51
[26] 52 55 56 57 60 61 62 63 64 65 67 70 71 72 73
detMCD: [1] 2 9 10 12 14 16 17 18 19 20 23 24 25 26 27 31 32 33 37 39 42 48 49 50 51
[26] 52 55 56 57 60 61 62 63 64 65 67 70 71 72 73
Difference detMCD - FastMCD:[1] 2 19 25
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=40); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): 16.9
Robust Estimate of Location:
POP MOR CAR DR GNP DEN TB
20.364 69.750 6.463 0.859 1.133 59.998 0.439
Robust Estimate of Covariance:
POP MOR CAR DR GNP DEN TB
POP 575.827 243.29 -12.910 -2.4098 -3.0456 160.82 0.4208
MOR 243.291 2376.56 -282.081 -33.9548 -33.9168 -718.68 -1.0522
CAR -12.910 -282.08 56.808 5.6651 6.4636 86.27 0.2616
DR -2.410 -33.95 5.665 0.9009 0.5568 18.60 0.0154
GNP -3.046 -33.92 6.464 0.5568 1.3929 10.67 0.0067
DEN 160.825 -718.68 86.269 18.6034 10.6747 2512.64 -1.1705
TB 0.421 -1.05 0.262 0.0154 0.0067 -1.17 0.0181
--------------------------------------------------------
Data Set n p h(alf) LOG(obj)
=============================================
wages FastMCD 36 9 23 25.658041
wages detMCD 36 9 23 25.722758
Best subsamples:
FastMCD: [1] 1 2 3 6 7 8 10 11 12 14 15 17 20 21 22 23 25 26 27 33 34 35 36
detMCD: [1] 1 2 3 6 7 8 10 11 14 15 17 20 21 22 23 25 27 29 31 33 34 35 36
Difference detMCD - FastMCD:[1] 29 31
Details about FastMCD : Outliers: 0
-------------
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=23); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = x, trace = trace)
Log(Det.): 25.7
Robust Estimate of Location:
HRS RATE ERSP ERNO NEIN ASSET AGE DEP
2140.17 2.85 1133.30 307.48 343.26 6539.43 39.57 2.44
SCHOOL
10.07
Robust Estimate of Covariance:
HRS RATE ERSP ERNO NEIN ASSET
HRS 4433.91 19.7358 -3585.03 -990.563 8227.4 184546
RATE 19.74 0.2393 8.06 1.048 59.2 1373
ERSP -3585.03 8.0565 12399.96 995.108 -4363.3 -78026
ERNO -990.56 1.0481 995.11 2190.581 -426.0 -9925
NEIN 8227.37 59.1712 -4363.27 -425.985 19585.3 441574
ASSET 184546.39 1373.0630 -78025.61 -9925.182 441574.2 10017473
AGE -46.58 -0.2052 18.34 19.517 -83.0 -1898
DEP -6.57 -0.0985 -2.85 0.499 -20.6 -471
SCHOOL 59.89 0.5677 7.54 -4.821 153.0 3541
AGE DEP SCHOOL
HRS -4.66e+01 -6.5659 59.885
RATE -2.05e-01 -0.0985 0.568
ERSP 1.83e+01 -2.8522 7.540
ERNO 1.95e+01 0.4986 -4.821
NEIN -8.30e+01 -20.6329 153.022
ASSET -1.90e+03 -471.1344 3540.557
AGE 7.72e-01 0.0412 -0.684
DEP 4.12e-02 0.0873 -0.240
SCHOOL -6.84e-01 -0.2402 1.453
--------------------------------------------------------
========================================================
> warnings() ## in one example n < 2 * p ..
Warning message:
In covMcd(X, use.correction = FALSE) :
n < 2 * p, i.e., possibly too small sample size
> ###' Test the exact fit property of CovMcd --------------------------------
>
> ##' generate "exact fit" data
> d.exact <- function(seed=seed, p=2) {
+ stopifnot(p >= 1)
+ set.seed(seed)
+ n1 <- 45
+ x1 <- matrix(rnorm(p*n1), nrow=n1, ncol=p)
+ x1[,p] <- x1[,p] + 3
+ n2 <- 55
+ m2 <- 3
+ x <- rbind(x1, cbind(matrix(rnorm((p-1)*n2), n2, p-1), rep(m2,n2)))
+ colnames(x) <- paste0("X", 1:p)
+ x
+ }
> plot(d.exact(18, p=2))
> pairs(d.exact(1234, p=3), gap=0.1)
> for(p in c(2,4))
+ for(sid in c(2, 4, 18, 1234)) {
+ cat("\nseed = ",sid,"; p = ",p,":\n")
+ d.x <- d.exact(sid, p=p)
+ d2 <- covMcd(d.x)
+ ## Gave error {for p=2, seeds 2, 4, 18 also on 64-bit}:
+ ## At line 729 of file rffastmcd.f
+ ## Fortran runtime error: Index '6' of dimension 1 of array 'z' above upper bound of 4
+ print(d2)
+ if(FALSE) ## FIXME fails when calling eigen() in "r6pack()"
+ d2. <- covMcd(d.x, nsamp = "deterministic", scalefn = Qn)
+ stopifnot(d2$singularity$kind == "on.hyperplane")
+ }
seed = 2 ; p = 2 :
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=51); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = d.x)
The 51-th order statistic of the absolute deviation of variable 2 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the line with equation 0 (x_i1-m_1) + 1 (x_i2-m_2) = 0 with (m_1,m_2)
the mean of these observations.
Log(Det.): -Inf
Robust Estimate of Location:
X1 X2
0.158 3.000
Robust Estimate of Covariance:
X1 X2
X1 4.26 0
X2 0.00 0
seed = 4 ; p = 2 :
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=51); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = d.x)
The 51-th order statistic of the absolute deviation of variable 2 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the line with equation 0 (x_i1-m_1) + 1 (x_i2-m_2) = 0 with (m_1,m_2)
the mean of these observations.
Log(Det.): -Inf
Robust Estimate of Location:
X1 X2
0.0133 3.0000
Robust Estimate of Covariance:
X1 X2
X1 3.59e+00 -8.53e-17
X2 -8.53e-17 0.00e+00
seed = 18 ; p = 2 :
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=51); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = d.x)
The 51-th order statistic of the absolute deviation of variable 2 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the line with equation 0 (x_i1-m_1) + 1 (x_i2-m_2) = 0 with (m_1,m_2)
the mean of these observations.
Log(Det.): -Inf
Robust Estimate of Location:
X1 X2
0.0277 3.0000
Robust Estimate of Covariance:
X1 X2
X1 3.01e+00 -1.14e-16
X2 -5.69e-17 0.00e+00
seed = 1234 ; p = 2 :
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=51); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = d.x)
The 51-th order statistic of the absolute deviation of variable 2 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the line with equation 0 (x_i1-m_1) + 1 (x_i2-m_2) = 0 with (m_1,m_2)
the mean of these observations.
Log(Det.): -Inf
Robust Estimate of Location:
X1 X2
0.0621 3.0000
Robust Estimate of Covariance:
X1 X2
X1 2.86e+00 -1.14e-16
X2 -1.14e-16 0.00e+00
seed = 2 ; p = 4 :
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=52); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = d.x)
The 52-th order statistic of the absolute deviation of variable 4 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the hyperplane with equation a_1*(x_i1 - m_1) + ... + a_p*(x_ip - m_p)
= 0 with (m_1, ..., m_p) the mean of these observations and
coefficients a_i from the vector a <- c(0, 0, 0, 1)
Log(Det.): -Inf
Robust Estimate of Location:
X1 X2 X3 X4
0.033 0.197 0.160 3.000
Robust Estimate of Covariance:
X1 X2 X3 X4
X1 2.52e+00 0.185 -0.113 -2.61e-16
X2 1.85e-01 2.236 -0.141 0.00e+00
X3 -1.13e-01 -0.141 1.789 0.00e+00
X4 -2.61e-16 0.000 0.000 0.00e+00
seed = 4 ; p = 4 :
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=52); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = d.x)
The 52-th order statistic of the absolute deviation of variable 4 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the hyperplane with equation a_1*(x_i1 - m_1) + ... + a_p*(x_ip - m_p)
= 0 with (m_1, ..., m_p) the mean of these observations and
coefficients a_i from the vector a <- c(0, 0, 0, 1)
Log(Det.): -Inf
Robust Estimate of Location:
X1 X2 X3 X4
-0.00568 -0.08741 -0.08413 3.00000
Robust Estimate of Covariance:
X1 X2 X3 X4
X1 2.24e+00 1.70e-01 -8.48e-02 1.07e-16
X2 1.70e-01 1.95e+00 -1.09e-01 1.49e-16
X3 -8.48e-02 -1.09e-01 2.20e+00 1.49e-16
X4 1.07e-16 7.45e-17 1.49e-16 0.00e+00
seed = 18 ; p = 4 :
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=52); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = d.x)
The 52-th order statistic of the absolute deviation of variable 4 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the hyperplane with equation a_1*(x_i1 - m_1) + ... + a_p*(x_ip - m_p)
= 0 with (m_1, ..., m_p) the mean of these observations and
coefficients a_i from the vector a <- c(0, 0, 0, 1)
Log(Det.): -Inf
Robust Estimate of Location:
X1 X2 X3 X4
-0.1567 0.0415 0.0109 3.0000
Robust Estimate of Covariance:
X1 X2 X3 X4
X1 2.59e+00 3.97e-02 -4.40e-01 -4.47e-16
X2 3.97e-02 2.21e+00 -3.44e-01 -7.45e-17
X3 -4.40e-01 -3.44e-01 2.55e+00 2.61e-16
X4 -4.47e-16 -7.45e-17 2.52e-16 0.00e+00
seed = 1234 ; p = 4 :
Minimum Covariance Determinant (MCD) estimator approximation.
Method: Fast MCD(alpha=0.5 ==> h=52); nsamp = 500; (n,k)mini = (300,5)
Call:
covMcd(x = d.x)
The 52-th order statistic of the absolute deviation of variable 4 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the hyperplane with equation a_1*(x_i1 - m_1) + ... + a_p*(x_ip - m_p)
= 0 with (m_1, ..., m_p) the mean of these observations and
coefficients a_i from the vector a <- c(0, 0, 0, 1)
Log(Det.): -Inf
Robust Estimate of Location:
X1 X2 X3 X4
0.1901 0.0538 0.0847 3.0000
Robust Estimate of Covariance:
X1 X2 X3 X4
X1 2.79e+00 2.21e-01 0.1668 5.96e-16
X2 2.21e-01 2.02e+00 -0.0216 1.49e-16
X3 1.67e-01 -2.16e-02 1.7319 0.00e+00
X4 5.96e-16 1.49e-16 0.0000 0.00e+00
> ## TODO: also get examples of other singularity$kind's
>
Warning messages:
1: In covMcd(d.x) :
The 51-th order statistic of the absolute deviation of variable 2 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the line with equation 0 (x_i1-m_1) + 1 (x_i2-m_2) = 0 with (m_1,m_2)
the mean of these observations.
2: In covMcd(d.x) :
The 51-th order statistic of the absolute deviation of variable 2 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the line with equation 0 (x_i1-m_1) + 1 (x_i2-m_2) = 0 with (m_1,m_2)
the mean of these observations.
3: In covMcd(d.x) :
The 51-th order statistic of the absolute deviation of variable 2 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the line with equation 0 (x_i1-m_1) + 1 (x_i2-m_2) = 0 with (m_1,m_2)
the mean of these observations.
4: In covMcd(d.x) :
The 51-th order statistic of the absolute deviation of variable 2 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the line with equation 0 (x_i1-m_1) + 1 (x_i2-m_2) = 0 with (m_1,m_2)
the mean of these observations.
5: In covMcd(d.x) :
The 52-th order statistic of the absolute deviation of variable 4 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the hyperplane with equation a_1*(x_i1 - m_1) + ... + a_p*(x_ip - m_p)
= 0 with (m_1, ..., m_p) the mean of these observations and
coefficients a_i from the vector a <- c(0, 0, 0, 1)
6: In covMcd(d.x) :
The 52-th order statistic of the absolute deviation of variable 4 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the hyperplane with equation a_1*(x_i1 - m_1) + ... + a_p*(x_ip - m_p)
= 0 with (m_1, ..., m_p) the mean of these observations and
coefficients a_i from the vector a <- c(0, 0, 0, 1)
7: In covMcd(d.x) :
The 52-th order statistic of the absolute deviation of variable 4 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the hyperplane with equation a_1*(x_i1 - m_1) + ... + a_p*(x_ip - m_p)
= 0 with (m_1, ..., m_p) the mean of these observations and
coefficients a_i from the vector a <- c(0, 0, 0, 1)
8: In covMcd(d.x) :
The 52-th order statistic of the absolute deviation of variable 4 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the hyperplane with equation a_1*(x_i1 - m_1) + ... + a_p*(x_ip - m_p)
= 0 with (m_1, ..., m_p) the mean of these observations and
coefficients a_i from the vector a <- c(0, 0, 0, 1)
> ## ----------- including simple "exactfit" (code = 3)
> warnings()
Warning messages:
1: In covMcd(d.x) :
The 51-th order statistic of the absolute deviation of variable 2 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the line with equation 0 (x_i1-m_1) + 1 (x_i2-m_2) = 0 with (m_1,m_2)
the mean of these observations.
2: In covMcd(d.x) :
The 51-th order statistic of the absolute deviation of variable 2 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the line with equation 0 (x_i1-m_1) + 1 (x_i2-m_2) = 0 with (m_1,m_2)
the mean of these observations.
3: In covMcd(d.x) :
The 51-th order statistic of the absolute deviation of variable 2 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the line with equation 0 (x_i1-m_1) + 1 (x_i2-m_2) = 0 with (m_1,m_2)
the mean of these observations.
4: In covMcd(d.x) :
The 51-th order statistic of the absolute deviation of variable 2 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the line with equation 0 (x_i1-m_1) + 1 (x_i2-m_2) = 0 with (m_1,m_2)
the mean of these observations.
5: In covMcd(d.x) :
The 52-th order statistic of the absolute deviation of variable 4 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the hyperplane with equation a_1*(x_i1 - m_1) + ... + a_p*(x_ip - m_p)
= 0 with (m_1, ..., m_p) the mean of these observations and
coefficients a_i from the vector a <- c(0, 0, 0, 1)
6: In covMcd(d.x) :
The 52-th order statistic of the absolute deviation of variable 4 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the hyperplane with equation a_1*(x_i1 - m_1) + ... + a_p*(x_ip - m_p)
= 0 with (m_1, ..., m_p) the mean of these observations and
coefficients a_i from the vector a <- c(0, 0, 0, 1)
7: In covMcd(d.x) :
The 52-th order statistic of the absolute deviation of variable 4 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the hyperplane with equation a_1*(x_i1 - m_1) + ... + a_p*(x_ip - m_p)
= 0 with (m_1, ..., m_p) the mean of these observations and
coefficients a_i from the vector a <- c(0, 0, 0, 1)
8: In covMcd(d.x) :
The 52-th order statistic of the absolute deviation of variable 4 is
zero.
There are 55 observations (in the entire dataset of 100 obs.) lying on
the hyperplane with equation a_1*(x_i1 - m_1) + ... + a_p*(x_ip - m_p)
= 0 with (m_1, ..., m_p) the mean of these observations and
coefficients a_i from the vector a <- c(0, 0, 0, 1)
>
> showProc.time()
Time (user system elapsed): 1.78 0.09 1.87
> if(!robustbase:::doExtras()) quit()
> proc.time()
user system elapsed
5.54 0.62 6.15