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Type 'q()' to quit R. > ## Test the exact fit property of CovMcd > doexactfit <- function(){ + exact <-function(seed=1234){ + + set.seed(seed) + + n1 <- 45 + p <- 2 + x1 <- matrix(rnorm(p*n1),nrow=n1, ncol=p) + x1[,p] <- x1[,p] + 3 + n2 <- 55 + m1 <- 0 + m2 <- 3 + x2 <- cbind(rnorm(n2),rep(m2,n2)) + x<-rbind(x1,x2) + colnames(x) <- c("X1","X2") + x + } + print(CovMcd(exact())) + } > > dodata <- function(nrep=1, time=FALSE, short=FALSE, full=TRUE, method = c("FASTMCD","MASS", "deterministic", "exact", "MRCD")){ + ##@bdescr + ## Test the function covMcd() on the literature datasets: + ## + ## Call CovMcd() for all regression datasets available in rrcov and print: + ## - execution time (if time == TRUE) + ## - objective fucntion + ## - best subsample found (if short == false) + ## - outliers identified (with cutoff 0.975) (if short == false) + ## - estimated center and covarinance matrix if full == TRUE) + ## + ##@edescr + ## + ##@in nrep : [integer] number of repetitions to use for estimating the + ## (average) execution time + ##@in time : [boolean] whether to evaluate the execution time + ##@in short : [boolean] whether to do short output (i.e. only the + ## objective function value). If short == FALSE, + ## the best subsample and the identified outliers are + ## printed. See also the parameter full below + ##@in full : [boolean] whether to print the estimated cente and covariance matrix + ##@in method : [character] select a method: one of (FASTMCD, MASS) + + doest <- function(x, xname, nrep=1){ + n <- dim(x)[1] + p <- dim(x)[2] + if(method == "MASS"){ + mcd<-cov.mcd(x) + quan <- as.integer(floor((n + p + 1)/2)) #default: floor((n+p+1)/2) + } + else{ + mcd <- if(method=="deterministic") CovMcd(x, nsamp="deterministic", trace=FALSE) + else if(method=="exact") CovMcd(x, nsamp="exact", trace=FALSE) + else if(method=="MRCD") CovMrcd(x, trace=FALSE) + else CovMcd(x, trace=FALSE) + quan <- as.integer(mcd@quan) + } + + crit <- mcd@crit + + if(time){ + xtime <- system.time(dorep(x, nrep, method))[1]/nrep + xres <- sprintf("%3d %3d %3d %12.6f %10.3f\n", dim(x)[1], dim(x)[2], quan, crit, xtime) + } + else{ + xres <- sprintf("%3d %3d %3d %12.6f\n", dim(x)[1], dim(x)[2], quan, crit) + } + lpad<-lname-nchar(xname) + cat(pad.right(xname,lpad), xres) + + if(!short){ + cat("Best subsample: \n") + if(length(mcd@best) > 150) + cat("Too long... \n") + else + print(mcd@best) + + ibad <- which(mcd@wt==0) + names(ibad) <- NULL + nbad <- length(ibad) + cat("Outliers: ",nbad,"\n") + if(nbad > 0 & nbad < 150) + print(ibad) + else + cat("Too many to print ... \n") + if(full){ + cat("-------------\n") + show(mcd) + } + cat("--------------------------------------------------------\n") + } + } + + options(digits = 5) + set.seed(101) # <<-- sub-sampling algorithm now based on R's RNG and seed + + lname <- 20 + + ## VT::15.09.2013 - this will render the output independent + ## from the version of the package + suppressPackageStartupMessages(library(rrcov)) + + method <- match.arg(method) + if(method == "MASS") + library(MASS) + + data(Animals, package = "MASS") + brain <- Animals[c(1:24, 26:25, 27:28),] + + data(fish) + data(pottery) + data(rice) + data(un86) + data(wages) + + tmp <- sys.call() + cat("\nCall: ", deparse(substitute(tmp)),"\n") + + cat("Data Set n p Half LOG(obj) Time\n") + cat("========================================================\n") + + if(method=="exact") + { + ## only small data sets + doest(heart[, 1:2], data(heart), nrep) + doest(starsCYG, data(starsCYG), nrep) + doest(data.matrix(subset(phosphor, select = -plant)), data(phosphor), nrep) + doest(data.matrix(subset(coleman, select = -Y)), data(coleman), nrep) + doest(data.matrix(subset(salinity, select = -Y)), data(salinity), nrep) + doest(data.matrix(subset(wood, select = -y)), data(wood), nrep) + doest(brain, "Animals", nrep) + doest(lactic, data(lactic), nrep) + doest(pension, data(pension), nrep) + doest(data.matrix(subset(vaso, select = -Y)), data(vaso), nrep) + doest(stack.x, data(stackloss), nrep) + doest(pilot, data(pilot), nrep) + } else + { + doest(heart[, 1:2], data(heart), nrep) + doest(starsCYG, data(starsCYG), nrep) + doest(data.matrix(subset(phosphor, select = -plant)), data(phosphor), nrep) + doest(stack.x, data(stackloss), nrep) + doest(data.matrix(subset(coleman, select = -Y)), data(coleman), nrep) + doest(data.matrix(subset(salinity, select = -Y)), data(salinity), nrep) + doest(data.matrix(subset(wood, select = -y)), data(wood), nrep) + doest(data.matrix(subset(hbk, select = -Y)),data(hbk), nrep) + + doest(brain, "Animals", nrep) + ## doest(milk, data(milk), nrep) # difference between 386 and x64 + doest(bushfire, data(bushfire), nrep) + + doest(lactic, data(lactic), nrep) + doest(pension, data(pension), nrep) + ## doest(pilot, data(pilot), nrep) # difference between 386 and x64 + + if(method != "MRCD") # these two are quite slow for MRCD, especially the second one + { + doest(radarImage, data(radarImage), nrep) + doest(NOxEmissions, data(NOxEmissions), nrep) + } + + doest(data.matrix(subset(vaso, select = -Y)), data(vaso), nrep) + doest(data.matrix(subset(wagnerGrowth, select = -Period)), data(wagnerGrowth), nrep) + + doest(data.matrix(subset(fish, select = -Species)), data(fish), nrep) + doest(data.matrix(subset(pottery, select = -origin)), data(pottery), nrep) + doest(rice, data(rice), nrep) + doest(un86, data(un86), nrep) + + doest(wages, data(wages), nrep) + + ## from package 'datasets' + doest(airquality[,1:4], data(airquality), nrep) + doest(attitude, data(attitude), nrep) + doest(attenu, data(attenu), nrep) + doest(USJudgeRatings, data(USJudgeRatings), nrep) + doest(USArrests, data(USArrests), nrep) + doest(longley, data(longley), nrep) + doest(Loblolly, data(Loblolly), nrep) + doest(quakes[,1:4], data(quakes), nrep) + } + cat("========================================================\n") + } > > dogen <- function(nrep=1, eps=0.49, method=c("FASTMCD", "MASS")){ + + doest <- function(x, nrep=1){ + gc() + xtime <- system.time(dorep(x, nrep, method))[1]/nrep + cat(sprintf("%6d %3d %10.2f\n", dim(x)[1], dim(x)[2], xtime)) + xtime + } + + set.seed(1234) + + ## VT::15.09.2013 - this will render the output independent + ## from the version of the package + suppressPackageStartupMessages(library(rrcov)) + + library(MASS) + method <- match.arg(method) + + ap <- c(2, 5, 10, 20, 30) + an <- c(100, 500, 1000, 10000, 50000) + + tottime <- 0 + cat(" n p Time\n") + cat("=====================\n") + for(i in 1:length(an)) { + for(j in 1:length(ap)) { + n <- an[i] + p <- ap[j] + if(5*p <= n){ + xx <- gendata(n, p, eps) + X <- xx$X + tottime <- tottime + doest(X, nrep) + } + } + } + + cat("=====================\n") + cat("Total time: ", tottime*nrep, "\n") + } > > docheck <- function(n, p, eps){ + xx <- gendata(n,p,eps) + mcd <- CovMcd(xx$X) + check(mcd, xx$xind) + } > > check <- function(mcd, xind){ + ## check if mcd is robust w.r.t xind, i.e. check how many of xind + ## did not get zero weight + mymatch <- xind %in% which(mcd@wt == 0) + length(xind) - length(which(mymatch)) + } > > dorep <- function(x, nrep=1, method=c("FASTMCD","MASS", "deterministic", "exact", "MRCD")){ + + method <- match.arg(method) + for(i in 1:nrep) + if(method == "MASS") + cov.mcd(x) + else + { + if(method=="deterministic") CovMcd(x, nsamp="deterministic", trace=FALSE) + else if(method=="exact") CovMcd(x, nsamp="exact", trace=FALSE) + else if(method=="MRCD") CovMrcd(x, trace=FALSE) + else CovMcd(x, trace=FALSE) + } + } > > #### gendata() #### > # Generates a location contaminated multivariate > # normal sample of n observations in p dimensions > # (1-eps)*Np(0,Ip) + eps*Np(m,Ip) > # where > # m = (b,b,...,b) > # Defaults: eps=0 and b=10 > # > gendata <- function(n,p,eps=0,b=10){ + + if(missing(n) || missing(p)) + stop("Please specify (n,p)") + if(eps < 0 || eps >= 0.5) + stop(message="eps must be in [0,0.5)") + X <- mvrnorm(n,rep(0,p),diag(1,nrow=p,ncol=p)) + nbad <- as.integer(eps * n) + if(nbad > 0){ + Xbad <- mvrnorm(nbad,rep(b,p),diag(1,nrow=p,ncol=p)) + xind <- sample(n,nbad) + X[xind,] <- Xbad + } + list(X=X, xind=xind) + } > > pad.right <- function(z, pads) + { + ### Pads spaces to right of text + padding <- paste(rep(" ", pads), collapse = "") + paste(z, padding, sep = "") + } > > whatis<-function(x){ + if(is.data.frame(x)) + cat("Type: data.frame\n") + else if(is.matrix(x)) + cat("Type: matrix\n") + else if(is.vector(x)) + cat("Type: vector\n") + else + cat("Type: don't know\n") + } > > ## VT::15.09.2013 - this will render the output independent > ## from the version of the package > suppressPackageStartupMessages(library(rrcov)) > > dodata() Call: dodata() Data Set n p Half LOG(obj) Time ======================================================== heart 12 2 7 5.678742 Best subsample: [1] 1 3 4 5 7 9 11 Outliers: 0 Too many to print ... ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=7); nsamp = 500; (n,k)mini = (300,5) Robust Estimate of Location: height weight 38.3 33.1 Robust Estimate of Covariance: height weight height 135 259 weight 259 564 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=25); nsamp = 500; (n,k)mini = (300,5) 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 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=10); nsamp = 500; (n,k)mini = (300,5) Robust Estimate of Location: inorg organic 13.4 38.8 Robust Estimate of Covariance: inorg organic inorg 129 130 organic 130 182 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=12); nsamp = 500; (n,k)mini = (300,5) 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 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=13); nsamp = 500; (n,k)mini = (300,5) 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 1.786 -0.266 0.151 0.075 fatherWc 1.786 1303.382 330.496 12.604 34.503 sstatus -0.266 330.496 119.888 3.833 10.131 teacherSc 0.151 12.604 3.833 0.785 0.555 motherLev 0.075 34.503 10.131 0.555 1.043 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=16); nsamp = 500; (n,k)mini = (300,5) 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 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=13); nsamp = 500; (n,k)mini = (300,5) 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 1.00e-02 1.88e-03 3.15e-03 -5.86e-04 -1.63e-03 x2 1.88e-03 4.85e-04 1.27e-03 -5.20e-05 2.36e-05 x3 3.15e-03 1.27e-03 6.63e-03 -8.71e-04 3.52e-04 x4 -5.86e-04 -5.20e-05 -8.71e-04 2.85e-03 1.83e-03 x5 -1.63e-03 2.36e-05 3.52e-04 1.83e-03 2.77e-03 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=39); nsamp = 500; (n,k)mini = (300,5) 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 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=15); nsamp = 500; (n,k)mini = (300,5) Robust Estimate of Location: body brain 18.7 64.9 Robust Estimate of Covariance: body brain body 929 1576 brain 1576 5646 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=22); nsamp = 500; (n,k)mini = (300,5) 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 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=11); nsamp = 500; (n,k)mini = (300,5) 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 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=10); nsamp = 500; (n,k)mini = (300,5) Robust Estimate of Location: Income Reserves 52.3 560.9 Robust Estimate of Covariance: Income Reserves Income 1420 11932 Reserves 11932 208643 -------------------------------------------------------- radarImage 1573 5 789 36.694425 Best subsample: Too long... Outliers: 117 [1] 164 237 238 242 261 262 351 450 451 462 480 481 509 516 535 [16] 542 572 597 620 643 654 669 697 737 802 803 804 818 832 833 [31] 834 862 863 864 892 900 939 989 1029 1064 1123 1132 1145 1202 1223 [46] 1224 1232 1233 1249 1250 1258 1259 1267 1303 1347 1357 1368 1375 1376 1393 [61] 1394 1402 1403 1411 1417 1419 1420 1428 1436 1443 1444 1453 1470 1479 1487 [76] 1492 1504 1510 1511 1512 1517 1518 1519 1520 1521 1522 1525 1526 1527 1528 [91] 1530 1532 1534 1543 1544 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 [106] 1557 1558 1561 1562 1564 1565 1566 1567 1569 1570 1571 1573 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=789); nsamp = 500; (n,k)mini = (300,5) Robust Estimate of Location: X.coord Y.coord Band.1 Band.2 Band.3 52.80 35.12 6.77 18.44 8.90 Robust Estimate of Covariance: X.coord Y.coord Band.1 Band.2 Band.3 X.coord 123.6 23.0 -361.9 -197.1 -22.5 Y.coord 23.0 400.6 34.3 -191.1 -39.1 Band.1 -361.9 34.3 27167.9 8178.8 473.7 Band.2 -197.1 -191.1 8178.8 26021.8 952.4 Band.3 -22.5 -39.1 473.7 952.4 4458.4 -------------------------------------------------------- NOxEmissions 8088 4 4046 2.474539 Best subsample: Too long... Outliers: 2156 Too many to print ... ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=4046); nsamp = 500; (n,k)mini = (300,5) Robust Estimate of Location: julday LNOx LNOxEm sqrtWS 168.19 4.73 7.91 1.37 Robust Estimate of Covariance: julday LNOx LNOxEm sqrtWS julday 9180.6297 12.0306 0.7219 -10.1273 LNOx 12.0306 0.4721 0.1418 -0.1526 LNOxEm 0.7219 0.1418 0.2516 0.0438 sqrtWS -10.1273 -0.1526 0.0438 0.2073 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=21); nsamp = 500; (n,k)mini = (300,5) 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 -------------------------------------------------------- wagnerGrowth 63 6 35 6.572208 Best subsample: [1] 2 3 4 5 6 7 9 10 11 12 13 14 16 17 18 20 23 25 27 31 32 35 36 38 44 [26] 48 51 52 53 54 55 56 57 60 62 Outliers: 13 [1] 1 8 15 21 22 28 29 33 42 43 46 50 63 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=35); nsamp = 500; (n,k)mini = (300,5) Robust Estimate of Location: Region PA GPA HS GHS y 11.00 33.66 -2.00 2.48 0.31 7.48 Robust Estimate of Covariance: Region PA GPA HS GHS y Region 35.5615 17.9337 -0.5337 -0.9545 -0.3093 -14.0090 PA 17.9337 27.7333 -4.9017 -1.4174 0.0343 -28.7040 GPA -0.5337 -4.9017 5.3410 0.2690 -0.1484 4.0006 HS -0.9545 -1.4174 0.2690 0.8662 -0.0454 2.9024 GHS -0.3093 0.0343 -0.1484 -0.0454 0.1772 0.7457 y -14.0090 -28.7040 4.0006 2.9024 0.7457 82.6877 -------------------------------------------------------- fish 159 6 82 8.879005 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 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 Outliers: 63 [1] 30 39 40 41 42 62 63 64 65 66 68 69 70 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 99 100 101 102 103 104 105 141 143 144 145 147 148 149 150 151 152 153 [58] 154 155 156 157 158 159 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=82); nsamp = 500; (n,k)mini = (300,5) 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 69082.99 1477.81 1613.64 1992.62 1439.32 -62.12 Length1 1477.81 34.68 37.61 45.51 28.82 -1.31 Length2 1613.64 37.61 40.88 49.52 31.81 -1.40 Length3 1992.62 45.51 49.52 61.16 42.65 -2.25 Height 1439.32 28.82 31.81 42.65 46.74 -2.82 Width -62.12 -1.31 -1.40 -2.25 -2.82 1.01 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=17); nsamp = 500; (n,k)mini = (300,5) 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 20.58227 2.28743 -0.02039 2.12648 -1.80227 0.08821 AL 2.28743 4.03605 -0.63021 -2.49966 0.20842 -0.02038 FE -0.02039 -0.63021 0.27803 0.53382 -0.35125 0.01427 MG 2.12648 -2.49966 0.53382 2.79561 -0.15786 0.02847 CA -1.80227 0.20842 -0.35125 -0.15786 1.23240 -0.03465 TI 0.08821 -0.02038 0.01427 0.02847 -0.03465 0.00175 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=56); nsamp = 500; (n,k)mini = (300,5) 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 -------------------------------------------------------- un86 73 7 40 17.009322 Best subsample: [1] 1 2 9 10 12 14 16 17 18 20 23 24 26 27 31 32 37 39 41 42 45 47 48 49 50 [26] 51 52 55 56 60 61 62 63 64 65 67 70 71 72 73 Outliers: 30 [1] 3 4 5 6 7 8 11 13 15 19 21 22 28 29 30 34 35 36 38 40 43 44 46 53 54 [26] 58 59 66 68 69 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=40); nsamp = 500; (n,k)mini = (300,5) Robust Estimate of Location: POP MOR CAR DR GNP DEN TB 20.740 71.023 6.435 0.817 1.146 56.754 0.441 Robust Estimate of Covariance: POP MOR CAR DR GNP DEN POP 582.4034 224.9343 -12.6722 -1.6729 -3.3664 226.1952 MOR 224.9343 2351.3907 -286.9504 -32.0743 -35.5649 -527.4684 CAR -12.6722 -286.9504 58.1190 5.7393 6.6365 83.6180 DR -1.6729 -32.0743 5.7393 0.8339 0.5977 12.1938 GNP -3.3664 -35.5649 6.6365 0.5977 1.4175 13.0709 DEN 226.1952 -527.4684 83.6180 12.1938 13.0709 2041.5809 TB 0.4002 -1.1807 0.2701 0.0191 0.0058 -0.9346 TB POP 0.4002 MOR -1.1807 CAR 0.2701 DR 0.0191 GNP 0.0058 DEN -0.9346 TB 0.0184 -------------------------------------------------------- wages 39 10 19 22.994272 Best subsample: [1] 1 2 6 7 8 9 10 11 12 13 14 15 17 18 19 25 26 27 28 Outliers: 9 [1] 4 5 6 24 28 30 32 33 34 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=19); nsamp = 500; (n,k)mini = (300,5) Robust Estimate of Location: HRS RATE ERSP ERNO NEIN ASSET AGE DEP 2153.37 2.87 1129.16 297.53 360.58 6876.58 39.48 2.36 RACE SCHOOL 38.88 10.17 Robust Estimate of Covariance: HRS RATE ERSP ERNO NEIN ASSET HRS 6.12e+03 1.73e+01 -1.67e+03 -2.06e+03 9.10e+03 2.02e+05 RATE 1.73e+01 2.52e-01 2.14e+01 -3.54e+00 5.85e+01 1.37e+03 ERSP -1.67e+03 2.14e+01 1.97e+04 7.76e+01 -1.71e+03 -1.41e+04 ERNO -2.06e+03 -3.54e+00 7.76e+01 2.06e+03 -2.02e+03 -4.83e+04 NEIN 9.10e+03 5.85e+01 -1.71e+03 -2.02e+03 2.02e+04 4.54e+05 ASSET 2.02e+05 1.37e+03 -1.41e+04 -4.83e+04 4.54e+05 1.03e+07 AGE -6.29e+01 -2.61e-01 4.83e+00 2.44e+01 -1.08e+02 -2.46e+03 DEP -6.17e+00 -7.05e-02 -2.13e+01 2.29e+00 -1.30e+01 -3.16e+02 RACE -2.17e+03 -9.46e+00 7.19e+02 5.59e+02 -3.95e+03 -8.77e+04 SCHOOL 7.12e+01 5.87e-01 5.39e+01 -2.14e+01 1.63e+02 3.79e+03 AGE DEP RACE SCHOOL HRS -6.29e+01 -6.17e+00 -2.17e+03 7.12e+01 RATE -2.61e-01 -7.05e-02 -9.46e+00 5.87e-01 ERSP 4.83e+00 -2.13e+01 7.19e+02 5.39e+01 ERNO 2.44e+01 2.29e+00 5.59e+02 -2.14e+01 NEIN -1.08e+02 -1.30e+01 -3.95e+03 1.63e+02 ASSET -2.46e+03 -3.16e+02 -8.77e+04 3.79e+03 AGE 1.01e+00 7.03e-02 2.39e+01 -9.52e-01 DEP 7.03e-02 4.62e-02 2.72e+00 -1.94e-01 RACE 2.39e+01 2.72e+00 8.74e+02 -3.09e+01 SCHOOL -9.52e-01 -1.94e-01 -3.09e+01 1.62e+00 -------------------------------------------------------- airquality 153 4 58 18.213499 Best subsample: [1] 3 22 24 25 28 29 32 33 35 36 37 38 39 40 41 42 43 44 46 [20] 47 48 49 50 52 56 57 58 59 60 64 66 67 68 69 71 72 73 74 [39] 76 78 80 82 83 84 86 87 89 90 91 92 93 94 95 97 98 105 109 [58] 110 Outliers: 14 [1] 8 9 15 18 20 21 23 24 28 30 48 62 117 148 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=58); nsamp = 500; (n,k)mini = (300,5) Robust Estimate of Location: Ozone Solar.R Wind Temp 43.2 192.9 9.6 80.5 Robust Estimate of Covariance: Ozone Solar.R Wind Temp Ozone 959.69 771.68 -60.92 198.38 Solar.R 771.68 7089.72 -1.72 95.75 Wind -60.92 -1.72 10.71 -11.96 Temp 198.38 95.75 -11.96 62.78 -------------------------------------------------------- attitude 30 7 19 24.442803 Best subsample: [1] 2 3 4 5 7 8 10 12 15 17 19 20 22 23 25 27 28 29 30 Outliers: 10 [1] 1 6 9 13 14 16 18 21 24 26 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=19); nsamp = 500; (n,k)mini = (300,5) Robust Estimate of Location: rating complaints privileges learning raises critical 67.1 68.0 52.4 57.6 67.2 77.4 advance 43.4 Robust Estimate of Covariance: rating complaints privileges learning raises critical advance rating 169.34 127.83 40.48 110.26 91.71 -3.59 53.84 complaints 127.83 156.80 52.65 110.97 96.56 7.27 76.03 privileges 40.48 52.65 136.91 92.38 69.00 9.53 87.98 learning 110.26 110.97 92.38 157.77 112.92 6.74 75.51 raises 91.71 96.56 69.00 112.92 112.79 4.91 70.22 critical -3.59 7.27 9.53 6.74 4.91 52.25 15.00 advance 53.84 76.03 87.98 75.51 70.22 15.00 93.11 -------------------------------------------------------- attenu 182 5 86 6.440834 Best subsample: [1] 68 69 70 71 72 73 74 75 76 77 79 82 83 84 85 86 87 88 89 [20] 90 91 92 101 102 103 104 106 107 109 110 111 112 113 114 115 116 117 118 [39] 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 [58] 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 [77] 157 158 159 160 161 162 163 164 165 166 Outliers: 61 [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 29 30 31 32 33 34 36 37 38 39 [39] 40 45 46 47 54 55 56 57 58 59 60 61 64 65 82 97 98 100 101 [58] 102 103 104 105 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=86); nsamp = 500; (n,k)mini = (300,5) Robust Estimate of Location: event mag station dist accel 18.624 5.752 67.861 22.770 0.141 Robust Estimate of Covariance: event mag station dist accel event 1.64e+01 -1.22e+00 5.59e+01 9.98e+00 -8.37e-02 mag -1.22e+00 4.13e-01 -3.19e+00 1.35e+00 1.22e-02 station 5.59e+01 -3.19e+00 1.03e+03 7.00e+01 5.56e-01 dist 9.98e+00 1.35e+00 7.00e+01 2.21e+02 -9.24e-01 accel -8.37e-02 1.22e-02 5.56e-01 -9.24e-01 9.62e-03 -------------------------------------------------------- USJudgeRatings 43 12 28 -47.889993 Best subsample: [1] 1 2 3 4 6 9 10 11 15 16 17 18 19 22 24 25 26 27 28 29 32 33 34 36 37 [26] 38 41 43 Outliers: 14 [1] 5 7 8 12 13 14 20 21 23 30 31 35 40 42 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=28); nsamp = 500; (n,k)mini = (300,5) Robust Estimate of Location: CONT INTG DMNR DILG CFMG DECI PREP FAMI ORAL WRIT PHYS RTEN 7.40 8.19 7.80 7.96 7.74 7.82 7.74 7.73 7.57 7.63 8.25 7.94 Robust Estimate of Covariance: CONT INTG DMNR DILG CFMG DECI PREP FAMI ORAL CONT 0.852 -0.266 -0.422 -0.155 -0.049 -0.074 -0.117 -0.119 -0.177 INTG -0.266 0.397 0.537 0.406 0.340 0.325 0.404 0.409 0.430 DMNR -0.422 0.537 0.824 0.524 0.458 0.437 0.520 0.504 0.569 DILG -0.155 0.406 0.524 0.486 0.426 0.409 0.506 0.515 0.511 CFMG -0.049 0.340 0.458 0.426 0.427 0.403 0.466 0.476 0.478 DECI -0.074 0.325 0.437 0.409 0.403 0.396 0.449 0.462 0.460 PREP -0.117 0.404 0.520 0.506 0.466 0.449 0.552 0.565 0.551 FAMI -0.119 0.409 0.504 0.515 0.476 0.462 0.565 0.594 0.571 ORAL -0.177 0.430 0.569 0.511 0.478 0.460 0.551 0.571 0.575 WRIT -0.159 0.427 0.549 0.515 0.480 0.461 0.556 0.580 0.574 PHYS -0.184 0.269 0.362 0.308 0.298 0.307 0.335 0.358 0.369 RTEN -0.260 0.472 0.642 0.519 0.467 0.455 0.539 0.554 0.573 WRIT PHYS RTEN CONT -0.159 -0.184 -0.260 INTG 0.427 0.269 0.472 DMNR 0.549 0.362 0.642 DILG 0.515 0.308 0.519 CFMG 0.480 0.298 0.467 DECI 0.461 0.307 0.455 PREP 0.556 0.335 0.539 FAMI 0.580 0.358 0.554 ORAL 0.574 0.369 0.573 WRIT 0.580 0.365 0.567 PHYS 0.365 0.300 0.378 RTEN 0.567 0.378 0.615 -------------------------------------------------------- USArrests 50 4 27 15.391648 Best subsample: [1] 4 7 9 12 13 14 15 16 19 21 23 26 27 29 30 32 34 35 36 38 41 42 43 45 46 [26] 49 50 Outliers: 11 [1] 2 3 5 6 10 18 24 28 33 37 47 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=27); nsamp = 500; (n,k)mini = (300,5) Robust Estimate of Location: Murder Assault UrbanPop Rape 6.71 145.42 65.06 17.88 Robust Estimate of Covariance: Murder Assault UrbanPop Rape Murder 16.1 269.3 20.3 25.2 Assault 269.3 6613.0 567.8 453.7 UrbanPop 20.3 567.8 225.4 47.7 Rape 25.2 453.7 47.7 50.9 -------------------------------------------------------- longley 16 7 12 12.747678 Best subsample: [1] 5 6 7 8 9 10 11 12 13 14 15 16 Outliers: 4 [1] 1 2 3 4 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=12); nsamp = 500; (n,k)mini = (300,5) Robust Estimate of Location: GNP.deflator GNP Unemployed Armed.Forces Population 106.5 430.6 328.2 295.0 120.2 Year Employed 1956.5 66.9 Robust Estimate of Covariance: GNP.deflator GNP Unemployed Armed.Forces Population GNP.deflator 108.5 1039.9 1231.9 -465.6 81.4 GNP 1039.9 10300.0 11161.6 -4277.6 803.4 Unemployed 1231.9 11161.6 19799.4 -5805.6 929.1 Armed.Forces -465.6 -4277.6 -5805.6 2805.5 -327.4 Population 81.4 803.4 929.1 -327.4 63.5 Year 51.6 504.3 595.6 -216.7 39.7 Employed 34.2 344.1 323.6 -149.5 26.2 Year Employed GNP.deflator 51.6 34.2 GNP 504.3 344.1 Unemployed 595.6 323.6 Armed.Forces -216.7 -149.5 Population 39.7 26.2 Year 25.1 16.7 Employed 16.7 12.4 -------------------------------------------------------- Loblolly 84 3 44 4.898174 Best subsample: [1] 1 2 4 7 8 10 13 14 19 20 21 25 26 28 31 32 33 34 37 38 39 40 43 44 45 [26] 46 49 50 51 55 56 58 61 62 64 67 68 69 73 74 75 79 80 81 Outliers: 31 [1] 5 6 11 12 15 17 18 23 24 29 30 35 36 41 42 47 48 53 54 59 60 65 66 70 71 [26] 72 76 77 78 83 84 ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=44); nsamp = 500; (n,k)mini = (300,5) Robust Estimate of Location: height age Seed 20.44 8.19 7.72 Robust Estimate of Covariance: height age Seed height 247.8 79.5 11.9 age 79.5 25.7 3.0 Seed 11.9 3.0 17.1 -------------------------------------------------------- quakes 1000 4 502 8.274369 Best subsample: Too long... Outliers: 265 Too many to print ... ------------- Call: CovMcd(x = x, trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=502); nsamp = 500; (n,k)mini = (300,5) Robust Estimate of Location: lat long depth mag -21.31 182.48 361.35 4.54 Robust Estimate of Covariance: lat long depth mag lat 1.47e+01 3.53e+00 1.34e+02 -2.52e-01 long 3.53e+00 4.55e+00 -3.63e+02 4.36e-02 depth 1.34e+02 -3.63e+02 4.84e+04 -1.29e+01 mag -2.52e-01 4.36e-02 -1.29e+01 1.38e-01 -------------------------------------------------------- ======================================================== > dodata(method="deterministic") Call: dodata(method = "deterministic") Data Set n p Half LOG(obj) Time ======================================================== heart 12 2 7 5.678742 Best subsample: [1] 1 3 4 5 7 9 11 Outliers: 0 Too many to print ... ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=7) Robust Estimate of Location: height weight 38.3 33.1 Robust Estimate of Covariance: height weight height 135 259 weight 259 564 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=25) 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 -------------------------------------------------------- phosphor 18 2 10 7.732906 Best subsample: [1] 2 4 5 7 8 9 11 12 14 16 Outliers: 1 [1] 6 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=10) Robust Estimate of Location: inorg organic 12.5 40.8 Robust Estimate of Covariance: inorg organic inorg 124 101 organic 101 197 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=12) 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 56.28 13.33 26.68 Water.Temp 13.33 8.28 6.98 Acid.Conc. 26.68 6.98 37.97 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=13) 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 2.956 2.146 0.447 0.110 fatherWc 2.956 1358.640 442.724 12.235 32.842 sstatus 2.146 442.724 205.590 6.464 11.382 teacherSc 0.447 12.235 6.464 1.179 0.510 motherLev 0.110 32.842 11.382 0.510 0.919 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=16) 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 -1.46156 X2 -0.00457 3.85051 -1.94604 X3 -1.46156 -1.94604 3.21424 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=13) 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 1.05e-02 1.81e-03 2.08e-03 -6.41e-04 -9.61e-04 x2 1.81e-03 5.55e-04 8.76e-04 -2.03e-04 -4.70e-05 x3 2.08e-03 8.76e-04 5.60e-03 -1.11e-03 -1.26e-05 x4 -6.41e-04 -2.03e-04 -1.11e-03 4.27e-03 2.60e-03 x5 -9.61e-04 -4.70e-05 -1.26e-05 2.60e-03 2.95e-03 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=39) 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 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=15) Robust Estimate of Location: body brain 18.7 64.9 Robust Estimate of Covariance: body brain body 929 1576 brain 1576 5646 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=22) 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 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=11) 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 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=10) Robust Estimate of Location: Income Reserves 52.3 560.9 Robust Estimate of Covariance: Income Reserves Income 1420 11932 Reserves 11932 208643 -------------------------------------------------------- radarImage 1573 5 789 36.694865 Best subsample: Too long... Outliers: 114 [1] 164 237 238 242 261 262 351 450 451 462 463 480 481 509 516 [16] 535 542 572 597 620 643 654 669 679 697 737 802 803 804 818 [31] 832 833 834 862 863 864 892 900 939 989 1029 1064 1123 1132 1145 [46] 1202 1223 1224 1232 1233 1249 1250 1258 1259 1267 1303 1347 1357 1368 1375 [61] 1376 1393 1394 1402 1411 1417 1419 1420 1428 1436 1443 1444 1453 1470 1504 [76] 1510 1511 1512 1518 1519 1520 1521 1522 1525 1526 1527 1528 1530 1532 1534 [91] 1543 1544 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1557 1558 1561 [106] 1562 1564 1565 1566 1567 1569 1570 1571 1573 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=789) Robust Estimate of Location: X.coord Y.coord Band.1 Band.2 Band.3 52.78 35.37 7.12 18.81 9.09 Robust Estimate of Covariance: X.coord Y.coord Band.1 Band.2 Band.3 X.coord 123.2 21.5 -363.9 -200.1 -24.3 Y.coord 21.5 410.7 46.5 -177.3 -33.4 Band.1 -363.9 46.5 27051.1 8138.9 469.3 Band.2 -200.1 -177.3 8138.9 25938.0 946.2 Band.3 -24.3 -33.4 469.3 946.2 4470.1 -------------------------------------------------------- NOxEmissions 8088 4 4046 2.474536 Best subsample: Too long... Outliers: 2152 Too many to print ... ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=4046) Robust Estimate of Location: julday LNOx LNOxEm sqrtWS 168.20 4.73 7.91 1.37 Robust Estimate of Covariance: julday LNOx LNOxEm sqrtWS julday 9176.2934 12.0355 0.7022 -10.1387 LNOx 12.0355 0.4736 0.1430 -0.1528 LNOxEm 0.7022 0.1430 0.2527 0.0436 sqrtWS -10.1387 -0.1528 0.0436 0.2074 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=21) 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 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=35) 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 35.1365 17.7291 -1.4003 -0.6554 -0.4728 -14.9305 PA 17.7291 28.4297 -5.5245 -1.2444 -0.0452 -29.6181 GPA -1.4003 -5.5245 5.2170 0.3954 -0.2152 3.8252 HS -0.6554 -1.2444 0.3954 0.7273 -0.0107 2.1514 GHS -0.4728 -0.0452 -0.2152 -0.0107 0.1728 0.8440 y -14.9305 -29.6181 3.8252 2.1514 0.8440 79.0511 -------------------------------------------------------- fish 159 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] 30 39 40 41 62 63 64 65 66 68 69 70 73 74 75 76 77 78 79 [20] 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 [39] 99 100 101 102 103 104 105 141 142 143 144 145 146 147 148 149 150 151 152 [58] 153 154 155 156 157 158 159 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=82) 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 64662.19 1412.34 1541.95 1917.21 1420.83 -61.15 Length1 1412.34 34.14 37.04 45.07 29.25 -1.26 Length2 1541.95 37.04 40.26 49.04 32.21 -1.34 Length3 1917.21 45.07 49.04 60.82 43.03 -2.15 Height 1420.83 29.25 32.21 43.03 46.50 -2.66 Width -61.15 -1.26 -1.34 -2.15 -2.66 1.02 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=17) 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 20.58227 2.28743 -0.02039 2.12648 -1.80227 0.08821 AL 2.28743 4.03605 -0.63021 -2.49966 0.20842 -0.02038 FE -0.02039 -0.63021 0.27803 0.53382 -0.35125 0.01427 MG 2.12648 -2.49966 0.53382 2.79561 -0.15786 0.02847 CA -1.80227 0.20842 -0.35125 -0.15786 1.23240 -0.03465 TI 0.08821 -0.02038 0.01427 0.02847 -0.03465 0.00175 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=56) 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 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=40) 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 POP 3.61e+02 1.95e+02 -6.28e+00 -1.91e-02 -2.07e+00 5.79e+01 MOR 1.95e+02 2.39e+03 -2.79e+02 -3.37e+01 -3.39e+01 -9.21e+02 CAR -6.28e+00 -2.79e+02 5.76e+01 5.77e+00 6.59e+00 7.81e+01 DR -1.91e-02 -3.37e+01 5.77e+00 9.07e-01 5.66e-01 1.69e+01 GNP -2.07e+00 -3.39e+01 6.59e+00 5.66e-01 1.42e+00 9.28e+00 DEN 5.79e+01 -9.21e+02 7.81e+01 1.69e+01 9.28e+00 3.53e+03 TB -6.09e-02 -9.93e-01 2.50e-01 1.98e-02 6.82e-03 -9.75e-01 TB POP -6.09e-02 MOR -9.93e-01 CAR 2.50e-01 DR 1.98e-02 GNP 6.82e-03 DEN -9.75e-01 TB 1.64e-02 -------------------------------------------------------- wages 39 10 19 23.119456 Best subsample: [1] 1 2 5 6 7 9 10 11 12 13 14 15 19 21 23 25 26 27 28 Outliers: 9 [1] 4 5 9 24 25 26 28 32 34 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=19) Robust Estimate of Location: HRS RATE ERSP ERNO NEIN ASSET AGE DEP 2161.89 2.95 1114.21 297.68 374.00 7269.37 39.13 2.43 RACE SCHOOL 36.13 10.39 Robust Estimate of Covariance: HRS RATE ERSP ERNO NEIN ASSET HRS 3.53e+03 8.31e+00 -5.96e+03 -6.43e+02 5.15e+03 1.12e+05 RATE 8.31e+00 1.78e-01 8.19e+00 2.70e+00 3.90e+01 8.94e+02 ERSP -5.96e+03 8.19e+00 1.90e+04 1.13e+03 -4.73e+03 -9.49e+04 ERNO -6.43e+02 2.70e+00 1.13e+03 1.80e+03 -3.56e+02 -7.33e+03 NEIN 5.15e+03 3.90e+01 -4.73e+03 -3.56e+02 1.38e+04 3.00e+05 ASSET 1.12e+05 8.94e+02 -9.49e+04 -7.33e+03 3.00e+05 6.62e+06 AGE -3.33e+01 -6.55e-02 8.33e+01 1.50e+00 -3.28e+01 -7.55e+02 DEP 4.50e+00 -4.01e-02 -2.77e+01 1.31e+00 -8.09e+00 -1.61e+02 RACE -1.30e+03 -6.06e+00 1.80e+03 1.48e+02 -2.58e+03 -5.59e+04 SCHOOL 3.01e+01 3.58e-01 -5.57e+00 2.84e+00 9.26e+01 2.10e+03 AGE DEP RACE SCHOOL HRS -3.33e+01 4.50e+00 -1.30e+03 3.01e+01 RATE -6.55e-02 -4.01e-02 -6.06e+00 3.58e-01 ERSP 8.33e+01 -2.77e+01 1.80e+03 -5.57e+00 ERNO 1.50e+00 1.31e+00 1.48e+02 2.84e+00 NEIN -3.28e+01 -8.09e+00 -2.58e+03 9.26e+01 ASSET -7.55e+02 -1.61e+02 -5.59e+04 2.10e+03 AGE 6.57e-01 -1.64e-01 1.13e+01 -2.67e-01 DEP -1.64e-01 9.20e-02 2.38e-01 -6.01e-02 RACE 1.13e+01 2.38e-01 5.73e+02 -1.67e+01 SCHOOL -2.67e-01 -6.01e-02 -1.67e+01 7.95e-01 -------------------------------------------------------- airquality 153 4 58 18.316848 Best subsample: [1] 2 3 8 10 24 25 28 32 33 35 36 37 38 39 40 41 42 43 46 [20] 47 48 49 50 52 54 56 57 58 59 60 66 67 69 71 72 73 76 78 [39] 81 82 84 86 87 89 90 91 92 95 97 98 100 101 105 106 108 109 110 [58] 111 Outliers: 10 [1] 8 9 15 18 24 30 48 62 117 148 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=58) Robust Estimate of Location: Ozone Solar.R Wind Temp 40.80 189.37 9.66 78.81 Robust Estimate of Covariance: Ozone Solar.R Wind Temp Ozone 935.54 857.76 -56.30 220.48 Solar.R 857.76 8507.83 1.36 155.13 Wind -56.30 1.36 9.90 -11.61 Temp 220.48 155.13 -11.61 84.00 -------------------------------------------------------- attitude 30 7 19 24.464288 Best subsample: [1] 2 3 4 5 7 8 10 11 12 15 17 19 21 22 23 25 27 28 29 Outliers: 8 [1] 6 9 13 14 16 18 24 26 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=19) Robust Estimate of Location: rating complaints privileges learning raises critical 64.4 65.2 51.0 55.5 65.9 77.4 advance 43.2 Robust Estimate of Covariance: rating complaints privileges learning raises critical advance rating 199.95 162.36 115.83 160.44 128.87 -13.55 66.20 complaints 162.36 204.84 130.33 170.66 150.19 16.28 96.66 privileges 115.83 130.33 181.31 152.63 106.56 4.52 91.44 learning 160.44 170.66 152.63 213.06 156.57 9.92 88.31 raises 128.87 150.19 106.56 156.57 152.05 23.10 84.00 critical -13.55 16.28 4.52 9.92 23.10 80.22 27.15 advance 66.20 96.66 91.44 88.31 84.00 27.15 95.51 -------------------------------------------------------- attenu 182 5 86 6.593068 Best subsample: [1] 41 42 43 44 48 49 51 68 70 72 73 74 75 76 77 82 83 84 85 [20] 86 87 88 89 90 91 92 101 102 103 104 106 107 109 110 111 112 113 114 [39] 115 116 117 119 120 121 122 124 125 126 127 128 129 130 131 132 133 134 135 [58] 136 137 138 139 140 141 144 145 146 147 148 149 150 151 152 153 154 155 156 [77] 157 158 159 160 161 162 163 164 165 166 Outliers: 49 [1] 1 2 4 5 6 7 8 9 10 11 12 13 14 15 16 19 20 21 22 [20] 23 24 25 27 28 29 30 31 32 33 40 45 47 59 60 61 64 65 78 [39] 82 83 97 98 100 101 102 103 104 105 117 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=86) Robust Estimate of Location: event mag station dist accel 17.122 5.798 63.461 25.015 0.131 Robust Estimate of Covariance: event mag station dist accel event 2.98e+01 -1.58e+00 9.49e+01 -8.36e+00 -3.59e-02 mag -1.58e+00 4.26e-01 -3.88e+00 3.13e+00 5.30e-03 station 9.49e+01 -3.88e+00 1.10e+03 2.60e+01 5.38e-01 dist -8.36e+00 3.13e+00 2.60e+01 2.66e+02 -9.23e-01 accel -3.59e-02 5.30e-03 5.38e-01 -9.23e-01 7.78e-03 -------------------------------------------------------- USJudgeRatings 43 12 28 -47.886937 Best subsample: [1] 2 3 4 6 9 10 11 15 16 18 19 22 24 25 26 27 28 29 30 32 33 34 36 37 38 [26] 40 41 43 Outliers: 14 [1] 1 5 7 8 12 13 14 17 20 21 23 31 35 42 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=28) Robust Estimate of Location: CONT INTG DMNR DILG CFMG DECI PREP FAMI ORAL WRIT PHYS RTEN 7.46 8.26 7.88 8.06 7.85 7.92 7.84 7.83 7.67 7.74 8.31 8.03 Robust Estimate of Covariance: CONT INTG DMNR DILG CFMG DECI PREP FAMI CONT 0.7363 -0.2916 -0.4193 -0.1943 -0.0555 -0.0690 -0.1703 -0.1727 INTG -0.2916 0.4179 0.5511 0.4167 0.3176 0.3102 0.4247 0.4279 DMNR -0.4193 0.5511 0.8141 0.5256 0.4092 0.3934 0.5294 0.5094 DILG -0.1943 0.4167 0.5256 0.4820 0.3904 0.3819 0.5054 0.5104 CFMG -0.0555 0.3176 0.4092 0.3904 0.3595 0.3368 0.4180 0.4206 DECI -0.0690 0.3102 0.3934 0.3819 0.3368 0.3310 0.4135 0.4194 PREP -0.1703 0.4247 0.5294 0.5054 0.4180 0.4135 0.5647 0.5752 FAMI -0.1727 0.4279 0.5094 0.5104 0.4206 0.4194 0.5752 0.6019 ORAL -0.2109 0.4453 0.5646 0.5054 0.4200 0.4121 0.5575 0.5735 WRIT -0.2033 0.4411 0.5466 0.5087 0.4222 0.4147 0.5592 0.5787 PHYS -0.1624 0.2578 0.3163 0.2833 0.2268 0.2362 0.3108 0.3284 RTEN -0.2622 0.4872 0.6324 0.5203 0.4145 0.4081 0.5488 0.5595 ORAL WRIT PHYS RTEN CONT -0.2109 -0.2033 -0.1624 -0.2622 INTG 0.4453 0.4411 0.2578 0.4872 DMNR 0.5646 0.5466 0.3163 0.6324 DILG 0.5054 0.5087 0.2833 0.5203 CFMG 0.4200 0.4222 0.2268 0.4145 DECI 0.4121 0.4147 0.2362 0.4081 PREP 0.5575 0.5592 0.3108 0.5488 FAMI 0.5735 0.5787 0.3284 0.5595 ORAL 0.5701 0.5677 0.3283 0.5688 WRIT 0.5677 0.5715 0.3268 0.5645 PHYS 0.3283 0.3268 0.2302 0.3308 RTEN 0.5688 0.5645 0.3308 0.6057 -------------------------------------------------------- USArrests 50 4 27 15.438912 Best subsample: [1] 4 7 12 13 14 15 16 19 21 23 25 26 27 29 30 32 34 35 36 38 41 43 45 46 48 [26] 49 50 Outliers: 7 [1] 2 5 6 10 24 28 33 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=27) Robust Estimate of Location: Murder Assault UrbanPop Rape 6.91 150.10 65.88 18.75 Robust Estimate of Covariance: Murder Assault UrbanPop Rape Murder 17.9 285.4 17.6 25.0 Assault 285.4 6572.8 524.9 465.0 UrbanPop 17.6 524.9 211.9 50.5 Rape 25.0 465.0 50.5 56.4 -------------------------------------------------------- longley 16 7 12 12.747678 Best subsample: [1] 5 6 7 8 9 10 11 12 13 14 15 16 Outliers: 4 [1] 1 2 3 4 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=12) Robust Estimate of Location: GNP.deflator GNP Unemployed Armed.Forces Population 106.5 430.6 328.2 295.0 120.2 Year Employed 1956.5 66.9 Robust Estimate of Covariance: GNP.deflator GNP Unemployed Armed.Forces Population GNP.deflator 108.5 1039.9 1231.9 -465.6 81.4 GNP 1039.9 10300.0 11161.6 -4277.6 803.4 Unemployed 1231.9 11161.6 19799.4 -5805.6 929.1 Armed.Forces -465.6 -4277.6 -5805.6 2805.5 -327.4 Population 81.4 803.4 929.1 -327.4 63.5 Year 51.6 504.3 595.6 -216.7 39.7 Employed 34.2 344.1 323.6 -149.5 26.2 Year Employed GNP.deflator 51.6 34.2 GNP 504.3 344.1 Unemployed 595.6 323.6 Armed.Forces -216.7 -149.5 Population 39.7 26.2 Year 25.1 16.7 Employed 16.7 12.4 -------------------------------------------------------- Loblolly 84 3 44 4.898174 Best subsample: [1] 1 2 4 7 8 10 13 14 19 20 21 25 26 28 31 32 33 34 37 38 39 40 43 44 45 [26] 46 49 50 51 55 56 58 61 62 64 67 68 69 73 74 75 79 80 81 Outliers: 31 [1] 5 6 11 12 15 17 18 23 24 29 30 35 36 41 42 47 48 53 54 59 60 65 66 70 71 [26] 72 76 77 78 83 84 ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=44) Robust Estimate of Location: height age Seed 20.44 8.19 7.72 Robust Estimate of Covariance: height age Seed height 247.8 79.5 11.9 age 79.5 25.7 3.0 Seed 11.9 3.0 17.1 -------------------------------------------------------- quakes 1000 4 502 8.274209 Best subsample: Too long... Outliers: 266 Too many to print ... ------------- Call: CovMcd(x = x, nsamp = "deterministic", trace = FALSE) -> Method: Deterministic MCD(alpha=0.5 ==> h=502) Robust Estimate of Location: lat long depth mag -21.34 182.47 360.58 4.54 Robust Estimate of Covariance: lat long depth mag lat 1.50e+01 3.58e+00 1.37e+02 -2.66e-01 long 3.58e+00 4.55e+00 -3.61e+02 4.64e-02 depth 1.37e+02 -3.61e+02 4.84e+04 -1.36e+01 mag -2.66e-01 4.64e-02 -1.36e+01 1.34e-01 -------------------------------------------------------- ======================================================== > dodata(method="exact") Call: dodata(method = "exact") Data Set n p Half LOG(obj) Time ======================================================== heart 12 2 7 5.678742 Best subsample: [1] 1 3 4 5 7 9 11 Outliers: 0 Too many to print ... ------------- Call: CovMcd(x = x, nsamp = "exact", trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=7); nsamp = exact; (n,k)mini = (300,5) Robust Estimate of Location: height weight 38.3 33.1 Robust Estimate of Covariance: height weight height 135 259 weight 259 564 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "exact", trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=25); nsamp = exact; (n,k)mini = (300,5) 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 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "exact", trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=10); nsamp = exact; (n,k)mini = (300,5) Robust Estimate of Location: inorg organic 13.4 38.8 Robust Estimate of Covariance: inorg organic inorg 129 130 organic 130 182 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "exact", trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=13); nsamp = exact; (n,k)mini = (300,5) 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 1.786 -0.266 0.151 0.075 fatherWc 1.786 1303.382 330.496 12.604 34.503 sstatus -0.266 330.496 119.888 3.833 10.131 teacherSc 0.151 12.604 3.833 0.785 0.555 motherLev 0.075 34.503 10.131 0.555 1.043 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "exact", trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=16); nsamp = exact; (n,k)mini = (300,5) 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 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "exact", trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=13); nsamp = exact; (n,k)mini = (300,5) 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 1.00e-02 1.88e-03 3.15e-03 -5.86e-04 -1.63e-03 x2 1.88e-03 4.85e-04 1.27e-03 -5.20e-05 2.36e-05 x3 3.15e-03 1.27e-03 6.63e-03 -8.71e-04 3.52e-04 x4 -5.86e-04 -5.20e-05 -8.71e-04 2.85e-03 1.83e-03 x5 -1.63e-03 2.36e-05 3.52e-04 1.83e-03 2.77e-03 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "exact", trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=15); nsamp = exact; (n,k)mini = (300,5) Robust Estimate of Location: body brain 18.7 64.9 Robust Estimate of Covariance: body brain body 929 1576 brain 1576 5646 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "exact", trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=11); nsamp = exact; (n,k)mini = (300,5) 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 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "exact", trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=10); nsamp = exact; (n,k)mini = (300,5) Robust Estimate of Location: Income Reserves 52.3 560.9 Robust Estimate of Covariance: Income Reserves Income 1420 11932 Reserves 11932 208643 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "exact", trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=21); nsamp = exact; (n,k)mini = (300,5) 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 -------------------------------------------------------- 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 ------------- Call: CovMcd(x = x, nsamp = "exact", trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=12); nsamp = exact; (n,k)mini = (300,5) 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 -------------------------------------------------------- pilot 20 2 11 6.487287 Best subsample: [1] 2 3 6 7 9 12 15 16 17 18 20 Outliers: 0 Too many to print ... ------------- Call: CovMcd(x = x, nsamp = "exact", trace = FALSE) -> Method: Fast MCD(alpha=0.5 ==> h=11); nsamp = exact; (n,k)mini = (300,5) Robust Estimate of Location: X Y 101.1 67.7 Robust Estimate of Covariance: X Y X 3344 1070 Y 1070 343 -------------------------------------------------------- ======================================================== > dodata(method="MRCD") Call: dodata(method = "MRCD") Data Set n p Half LOG(obj) Time ======================================================== heart 12 2 6 7.446266 Best subsample: [1] 1 3 4 7 9 11 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=6) Robust Estimate of Location: height weight 38.8 33.0 Robust Estimate of Covariance: height weight height 47.4 75.2 weight 75.2 155.4 -------------------------------------------------------- starsCYG 47 2 24 -5.862050 Best subsample: [1] 1 6 10 12 13 16 23 24 25 26 28 31 33 37 38 39 40 41 42 43 44 45 46 47 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=24) Robust Estimate of Location: log.Te log.light 4.44 5.05 Robust Estimate of Covariance: log.Te log.light log.Te 0.00867 0.02686 log.light 0.02686 0.41127 -------------------------------------------------------- phosphor 18 2 9 9.954788 Best subsample: [1] 4 7 8 9 11 12 13 14 16 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=9) Robust Estimate of Location: inorg organic 12.5 39.0 Robust Estimate of Covariance: inorg organic inorg 236 140 organic 140 172 -------------------------------------------------------- stackloss 21 3 11 7.991165 Best subsample: [1] 4 5 6 7 8 9 10 13 18 19 20 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=11) Robust Estimate of Location: Air.Flow Water.Temp Acid.Conc. 58.2 21.4 85.2 Robust Estimate of Covariance: Air.Flow Water.Temp Acid.Conc. Air.Flow 49.8 17.2 42.7 Water.Temp 17.2 13.8 25.2 Acid.Conc. 42.7 25.2 58.2 -------------------------------------------------------- coleman 20 5 10 5.212156 Best subsample: [1] 3 4 5 7 8 9 14 16 19 20 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=10) Robust Estimate of Location: salaryP fatherWc sstatus teacherSc motherLev 2.78 59.44 9.28 25.41 6.70 Robust Estimate of Covariance: salaryP fatherWc sstatus teacherSc motherLev salaryP 0.1582 -0.2826 0.4112 0.1754 0.0153 fatherWc -0.2826 902.9210 201.5815 -2.1236 18.8736 sstatus 0.4112 201.5815 65.4580 -0.3876 4.7794 teacherSc 0.1754 -2.1236 -0.3876 0.7233 -0.0322 motherLev 0.0153 18.8736 4.7794 -0.0322 0.5417 -------------------------------------------------------- salinity 28 3 14 3.586919 Best subsample: [1] 1 7 8 12 13 14 18 20 21 22 25 26 27 28 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=14) Robust Estimate of Location: X1 X2 X3 10.95 3.71 21.99 Robust Estimate of Covariance: X1 X2 X3 X1 14.153 0.718 -3.359 X2 0.718 3.565 -0.722 X3 -3.359 -0.722 1.607 -------------------------------------------------------- wood 20 5 10 -33.100492 Best subsample: [1] 1 2 3 5 11 14 15 17 18 20 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=10) Robust Estimate of Location: x1 x2 x3 x4 x5 0.572 0.120 0.504 0.545 0.899 Robust Estimate of Covariance: x1 x2 x3 x4 x5 x1 0.007543 0.001720 0.000412 -0.001230 -0.001222 x2 0.001720 0.000568 0.000355 -0.000533 -0.000132 x3 0.000412 0.000355 0.002478 0.000190 0.000811 x4 -0.001230 -0.000533 0.000190 0.002327 0.000967 x5 -0.001222 -0.000132 0.000811 0.000967 0.001894 -------------------------------------------------------- hbk 75 3 38 1.539545 Best subsample: [1] 15 17 18 19 20 21 22 23 24 26 27 29 32 33 35 36 38 40 41 43 48 49 50 51 54 [26] 55 56 58 59 63 64 66 67 70 71 72 73 74 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=38) Robust Estimate of Location: X1 X2 X3 1.60 2.37 1.64 Robust Estimate of Covariance: X1 X2 X3 X1 2.810 0.124 1.248 X2 0.124 1.017 0.208 X3 1.248 0.208 2.218 -------------------------------------------------------- Animals 28 2 14 16.278395 Best subsample: [1] 1 3 4 5 10 11 18 19 20 21 22 23 26 27 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=14) Robust Estimate of Location: body brain 19.5 56.8 Robust Estimate of Covariance: body brain body 2802 5179 brain 5179 13761 -------------------------------------------------------- bushfire 38 5 19 28.483413 Best subsample: [1] 1 2 3 4 5 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=19) Robust Estimate of Location: V1 V2 V3 V4 V5 103 145 287 221 281 Robust Estimate of Covariance: V1 V2 V3 V4 V5 V1 366 249 -1993 -503 -396 V2 249 252 -1223 -291 -233 V3 -1993 -1223 14246 3479 2718 V4 -503 -291 3479 1083 748 V5 -396 -233 2718 748 660 -------------------------------------------------------- lactic 20 2 10 2.593141 Best subsample: [1] 1 2 3 4 5 7 8 9 10 11 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=10) Robust Estimate of Location: X Y 2.60 3.63 Robust Estimate of Covariance: X Y X 8.13 13.54 Y 13.54 24.17 -------------------------------------------------------- pension 18 2 9 18.931204 Best subsample: [1] 2 3 4 5 6 8 9 11 12 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=9) Robust Estimate of Location: Income Reserves 45.7 466.9 Robust Estimate of Covariance: Income Reserves Income 2127 23960 Reserves 23960 348275 -------------------------------------------------------- vaso 39 2 20 -1.864710 Best subsample: [1] 3 4 8 14 18 20 21 22 23 24 25 26 27 28 33 34 35 37 38 39 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=20) Robust Estimate of Location: Volume Rate 1.14 1.77 Robust Estimate of Covariance: Volume Rate Volume 0.44943 -0.00465 Rate -0.00465 0.34480 -------------------------------------------------------- wagnerGrowth 63 6 32 9.287760 Best subsample: [1] 2 3 4 5 6 7 9 10 11 12 16 18 20 23 25 27 31 32 35 36 38 41 44 48 52 [26] 53 54 55 56 57 60 62 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=32) Robust Estimate of Location: Region PA GPA HS GHS y 10.719 33.816 -2.144 2.487 0.293 4.918 Robust Estimate of Covariance: Region PA GPA HS GHS y Region 56.7128 17.4919 -2.9710 -0.6491 -0.4545 -10.4287 PA 17.4919 29.9968 -7.6846 -1.3141 0.5418 -35.6434 GPA -2.9710 -7.6846 6.3238 1.1257 -0.4757 12.4707 HS -0.6491 -1.3141 1.1257 1.1330 -0.0915 3.3617 GHS -0.4545 0.5418 -0.4757 -0.0915 0.1468 -1.1228 y -10.4287 -35.6434 12.4707 3.3617 -1.1228 67.4215 -------------------------------------------------------- fish 159 6 79 22.142828 Best subsample: [1] 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 [20] 22 23 24 25 26 27 35 36 37 42 43 44 45 46 47 48 49 50 51 [39] 52 53 54 55 56 57 58 59 60 71 105 106 107 109 110 111 113 114 115 [58] 116 117 118 119 120 122 123 124 125 126 127 128 129 130 131 132 134 135 136 [77] 137 138 139 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=79) Robust Estimate of Location: Weight Length1 Length2 Length3 Height Width 291.7 23.8 25.9 28.9 30.4 14.7 Robust Estimate of Covariance: Weight Length1 Length2 Length3 Height Width Weight 77155.07 1567.55 1713.74 2213.16 1912.62 -103.97 Length1 1567.55 45.66 41.57 52.14 38.66 -2.39 Length2 1713.74 41.57 54.26 56.77 42.72 -2.55 Length3 2213.16 52.14 56.77 82.57 58.84 -3.65 Height 1912.62 38.66 42.72 58.84 70.51 -3.80 Width -103.97 -2.39 -2.55 -3.65 -3.80 1.19 -------------------------------------------------------- pottery 27 6 14 -6.897459 Best subsample: [1] 1 2 4 5 6 10 11 13 14 15 19 21 22 26 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=14) Robust Estimate of Location: SI AL FE MG CA TI 54.39 14.93 9.78 3.82 5.11 0.86 Robust Estimate of Covariance: SI AL FE MG CA TI SI 17.47469 -0.16656 0.39943 4.48192 -0.71153 0.06515 AL -0.16656 3.93154 -0.35738 -2.29899 0.14770 -0.02050 FE 0.39943 -0.35738 0.20434 0.37562 -0.22460 0.00943 MG 4.48192 -2.29899 0.37562 2.82339 -0.16027 0.02943 CA -0.71153 0.14770 -0.22460 -0.16027 0.88443 -0.01711 TI 0.06515 -0.02050 0.00943 0.02943 -0.01711 0.00114 -------------------------------------------------------- rice 105 6 53 -8.916472 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 54 55 59 60 65 67 70 72 76 79 80 81 [39] 82 83 84 85 86 90 92 93 94 95 97 98 99 101 105 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=53) Robust Estimate of Location: Favor Appearance Taste Stickiness -0.1741 0.0774 -0.0472 0.1868 Toughness Overall_evaluation -0.0346 -0.0683 Robust Estimate of Covariance: Favor Appearance Taste Stickiness Toughness Favor 0.402 0.306 0.378 0.364 -0.134 Appearance 0.306 0.508 0.474 0.407 -0.146 Taste 0.378 0.474 0.708 0.611 -0.258 Stickiness 0.364 0.407 0.611 0.795 -0.320 Toughness -0.134 -0.146 -0.258 -0.320 0.302 Overall_evaluation 0.453 0.536 0.746 0.745 -0.327 Overall_evaluation Favor 0.453 Appearance 0.536 Taste 0.746 Stickiness 0.745 Toughness -0.327 Overall_evaluation 0.963 -------------------------------------------------------- un86 73 7 37 19.832993 Best subsample: [1] 9 10 12 14 16 17 18 20 23 24 25 26 27 31 32 33 37 39 42 48 49 50 51 52 55 [26] 56 57 60 62 63 64 65 67 70 71 72 73 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=37) Robust Estimate of Location: POP MOR CAR DR GNP DEN TB 14.462 66.892 6.670 0.858 1.251 55.518 0.429 Robust Estimate of Covariance: POP MOR CAR DR GNP DEN POP 3.00e+02 1.58e+02 9.83e+00 2.74e+00 5.51e-01 6.87e+01 MOR 1.58e+02 2.96e+03 -4.24e+02 -4.72e+01 -5.40e+01 -1.01e+03 CAR 9.83e+00 -4.24e+02 9.12e+01 8.71e+00 1.13e+01 1.96e+02 DR 2.74e+00 -4.72e+01 8.71e+00 1.25e+00 1.03e+00 2.74e+01 GNP 5.51e-01 -5.40e+01 1.13e+01 1.03e+00 2.31e+00 2.36e+01 DEN 6.87e+01 -1.01e+03 1.96e+02 2.74e+01 2.36e+01 3.12e+03 TB 2.04e-02 -1.81e+00 3.42e-01 2.57e-02 2.09e-02 -6.88e-01 TB POP 2.04e-02 MOR -1.81e+00 CAR 3.42e-01 DR 2.57e-02 GNP 2.09e-02 DEN -6.88e-01 TB 2.59e-02 -------------------------------------------------------- wages 39 10 14 35.698016 Best subsample: [1] 1 2 5 6 9 10 11 13 15 19 23 25 26 28 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=14) Robust Estimate of Location: HRS RATE ERSP ERNO NEIN ASSET AGE DEP 2167.71 2.96 1113.50 300.43 382.29 7438.00 39.06 2.41 RACE SCHOOL 33.00 10.45 Robust Estimate of Covariance: HRS RATE ERSP ERNO NEIN ASSET HRS 1.97e+03 -4.14e-01 -4.71e+03 -6.58e+02 1.81e+03 3.84e+04 RATE -4.14e-01 1.14e-01 1.79e+01 3.08e+00 1.40e+01 3.57e+02 ERSP -4.71e+03 1.79e+01 1.87e+04 2.33e+03 -2.06e+03 -3.57e+04 ERNO -6.58e+02 3.08e+00 2.33e+03 5.36e+02 -3.42e+02 -5.56e+03 NEIN 1.81e+03 1.40e+01 -2.06e+03 -3.42e+02 5.77e+03 1.10e+05 ASSET 3.84e+04 3.57e+02 -3.57e+04 -5.56e+03 1.10e+05 2.86e+06 AGE -1.83e+01 1.09e-02 6.69e+01 8.78e+00 -5.07e+00 -1.51e+02 DEP 4.82e+00 -3.14e-02 -2.52e+01 -2.96e+00 -5.33e+00 -1.03e+02 RACE -5.67e+02 -1.33e+00 1.21e+03 1.81e+02 -9.13e+02 -1.96e+04 SCHOOL 5.33e+00 1.87e-01 1.86e+01 3.12e+00 3.20e+01 7.89e+02 AGE DEP RACE SCHOOL HRS -1.83e+01 4.82e+00 -5.67e+02 5.33e+00 RATE 1.09e-02 -3.14e-02 -1.33e+00 1.87e-01 ERSP 6.69e+01 -2.52e+01 1.21e+03 1.86e+01 ERNO 8.78e+00 -2.96e+00 1.81e+02 3.12e+00 NEIN -5.07e+00 -5.33e+00 -9.13e+02 3.20e+01 ASSET -1.51e+02 -1.03e+02 -1.96e+04 7.89e+02 AGE 5.71e-01 -1.56e-01 4.58e+00 -5.00e-02 DEP -1.56e-01 8.08e-02 -3.02e-01 -4.47e-02 RACE 4.58e+00 -3.02e-01 2.36e+02 -4.54e+00 SCHOOL -5.00e-02 -4.47e-02 -4.54e+00 4.23e-01 -------------------------------------------------------- airquality 153 4 56 21.136376 Best subsample: [1] 2 3 8 10 24 25 28 32 33 35 36 37 38 39 40 41 42 43 46 [20] 47 48 49 52 54 56 57 58 59 60 66 67 69 71 72 73 76 78 81 [39] 82 84 86 87 89 90 91 92 96 97 98 100 101 105 106 109 110 111 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=56) Robust Estimate of Location: Ozone Solar.R Wind Temp 41.84 197.21 8.93 80.39 Robust Estimate of Covariance: Ozone Solar.R Wind Temp Ozone 1480.7 1562.8 -99.9 347.3 Solar.R 1562.8 11401.2 -35.2 276.8 Wind -99.9 -35.2 11.4 -23.5 Temp 347.3 276.8 -23.5 107.7 -------------------------------------------------------- attitude 30 7 15 27.040805 Best subsample: [1] 2 3 4 5 7 8 10 12 15 19 22 23 25 27 28 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=15) Robust Estimate of Location: rating complaints privileges learning raises critical 65.8 66.5 50.1 56.1 66.7 78.1 advance 41.7 Robust Estimate of Covariance: rating complaints privileges learning raises critical advance rating 138.77 80.02 59.22 107.33 95.83 -1.24 54.36 complaints 80.02 97.23 50.59 99.50 79.15 -2.71 42.81 privileges 59.22 50.59 84.92 90.03 60.88 22.39 44.93 learning 107.33 99.50 90.03 187.67 128.71 15.48 63.67 raises 95.83 79.15 60.88 128.71 123.94 -1.46 49.98 critical -1.24 -2.71 22.39 15.48 -1.46 61.23 12.88 advance 54.36 42.81 44.93 63.67 49.98 12.88 48.61 -------------------------------------------------------- attenu 182 5 83 9.710111 Best subsample: [1] 41 42 43 44 48 49 51 68 70 72 73 74 75 76 77 82 83 84 85 [20] 86 87 88 89 90 91 92 101 102 103 104 106 107 109 110 111 112 113 114 [39] 115 116 117 121 122 124 125 126 127 128 129 130 131 132 133 134 135 136 137 [58] 138 139 140 141 144 145 146 147 148 149 150 151 152 153 155 156 157 158 159 [77] 160 161 162 163 164 165 166 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=83) Robust Estimate of Location: event mag station dist accel 18.940 5.741 67.988 23.365 0.124 Robust Estimate of Covariance: event mag station dist accel event 2.86e+01 -2.31e+00 1.02e+02 2.68e+01 -1.99e-01 mag -2.31e+00 6.17e-01 -7.03e+00 4.67e-01 2.59e-02 station 1.02e+02 -7.03e+00 1.66e+03 1.62e+02 7.96e-02 dist 2.68e+01 4.67e-01 1.62e+02 3.61e+02 -1.23e+00 accel -1.99e-01 2.59e-02 7.96e-02 -1.23e+00 9.42e-03 -------------------------------------------------------- USJudgeRatings 43 12 22 -23.463708 Best subsample: [1] 2 3 4 6 9 11 15 16 18 19 24 25 26 27 28 29 32 33 34 36 37 38 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=22) Robust Estimate of Location: CONT INTG DMNR DILG CFMG DECI PREP FAMI ORAL WRIT PHYS RTEN 7.24 8.42 8.10 8.19 7.95 8.00 7.96 7.96 7.81 7.89 8.40 8.20 Robust Estimate of Covariance: CONT INTG DMNR DILG CFMG DECI PREP CONT 0.61805 -0.05601 -0.09540 0.00694 0.09853 0.06261 0.03939 INTG -0.05601 0.23560 0.27537 0.20758 0.16603 0.17281 0.21128 DMNR -0.09540 0.27537 0.55349 0.28872 0.24014 0.24293 0.28886 DILG 0.00694 0.20758 0.28872 0.34099 0.23502 0.23917 0.29672 CFMG 0.09853 0.16603 0.24014 0.23502 0.31649 0.23291 0.27651 DECI 0.06261 0.17281 0.24293 0.23917 0.23291 0.30681 0.27737 PREP 0.03939 0.21128 0.28886 0.29672 0.27651 0.27737 0.42020 FAMI 0.04588 0.20388 0.26072 0.29037 0.27179 0.27737 0.34857 ORAL 0.03000 0.21379 0.29606 0.28764 0.27338 0.27424 0.33503 WRIT 0.03261 0.20258 0.26931 0.27962 0.26382 0.26610 0.32677 PHYS -0.04485 0.13598 0.17659 0.16834 0.14554 0.16467 0.18948 RTEN 0.01543 0.22654 0.32117 0.27307 0.23826 0.24669 0.29450 FAMI ORAL WRIT PHYS RTEN CONT 0.04588 0.03000 0.03261 -0.04485 0.01543 INTG 0.20388 0.21379 0.20258 0.13598 0.22654 DMNR 0.26072 0.29606 0.26931 0.17659 0.32117 DILG 0.29037 0.28764 0.27962 0.16834 0.27307 CFMG 0.27179 0.27338 0.26382 0.14554 0.23826 DECI 0.27737 0.27424 0.26610 0.16467 0.24669 PREP 0.34857 0.33503 0.32677 0.18948 0.29450 FAMI 0.47232 0.33762 0.33420 0.19759 0.29015 ORAL 0.33762 0.40361 0.32208 0.19794 0.29544 WRIT 0.33420 0.32208 0.38733 0.19276 0.28184 PHYS 0.19759 0.19794 0.19276 0.20284 0.18097 RTEN 0.29015 0.29544 0.28184 0.18097 0.36877 -------------------------------------------------------- USArrests 50 4 25 17.834643 Best subsample: [1] 4 7 12 13 14 15 16 19 21 23 25 26 27 29 30 32 34 35 36 38 41 45 46 49 50 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=25) Robust Estimate of Location: Murder Assault UrbanPop Rape 5.38 121.68 63.80 16.33 Robust Estimate of Covariance: Murder Assault UrbanPop Rape Murder 17.8 316.3 48.5 31.1 Assault 316.3 6863.0 1040.0 548.9 UrbanPop 48.5 1040.0 424.8 93.6 Rape 31.1 548.9 93.6 63.8 -------------------------------------------------------- longley 16 7 8 31.147844 Best subsample: [1] 5 6 7 9 10 11 13 14 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=8) Robust Estimate of Location: GNP.deflator GNP Unemployed Armed.Forces Population 104.3 410.8 278.8 300.1 118.2 Year Employed 1955.4 66.5 Robust Estimate of Covariance: GNP.deflator GNP Unemployed Armed.Forces Population GNP.deflator 85.0 652.3 784.4 -370.7 48.7 GNP 652.3 7502.9 7328.6 -3414.2 453.9 Unemployed 784.4 7328.6 10760.3 -4646.7 548.1 Armed.Forces -370.7 -3414.2 -4646.7 2824.3 -253.9 Population 48.7 453.9 548.1 -253.9 40.2 Year 33.5 312.7 378.8 -176.1 23.4 Employed 23.9 224.8 263.6 -128.3 16.8 Year Employed GNP.deflator 33.5 23.9 GNP 312.7 224.8 Unemployed 378.8 263.6 Armed.Forces -176.1 -128.3 Population 23.4 16.8 Year 18.9 11.7 Employed 11.7 10.3 -------------------------------------------------------- Loblolly 84 3 42 11.163448 Best subsample: [1] 3 4 5 6 10 21 22 23 24 28 29 33 34 35 36 39 40 41 42 45 46 47 48 51 52 [26] 53 54 57 58 59 63 64 65 66 70 71 76 77 81 82 83 84 Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=42) Robust Estimate of Location: height age Seed 44.20 17.26 6.76 Robust Estimate of Covariance: height age Seed height 326.74 139.18 3.50 age 139.18 68.48 -2.72 Seed 3.50 -2.72 25.43 -------------------------------------------------------- quakes 1000 4 500 11.802478 Best subsample: Too long... Outliers: 0 Too many to print ... ------------- Call: CovMrcd(x = x, trace = FALSE) -> Method: Minimum Regularized Covariance Determinant MRCD(alpha=0.5 ==> h=500) Robust Estimate of Location: lat long depth mag -20.59 182.13 432.46 4.42 Robust Estimate of Covariance: lat long depth mag lat 15.841 5.702 -106.720 -0.441 long 5.702 7.426 -577.189 -0.136 depth -106.720 -577.189 66701.479 3.992 mag -0.441 -0.136 3.992 0.144 -------------------------------------------------------- ======================================================== > ##doexactfit() > > proc.time() user system elapsed 3.29 0.51 3.76