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Type 'q()' to quit R. > ## VT::15.09.2013 - this will render the output independent > ## from the version of the package > suppressPackageStartupMessages(library(rrcov)) > > library(MASS) > > dodata <- function(nrep = 1, time = FALSE, full = TRUE, method) { + doest <- function(x, xname, nrep = 1, method=c("sfast", "surreal", "bisquare", "rocke", "suser", "MM", "sdet")) { + + method <- match.arg(method) + + lname <- 20 + n <- dim(x)[1] + p <- dim(x)[2] + + mm <- if(method == "MM") CovMMest(x) else CovSest(x, method=method) + + crit <- log(mm@crit) + + xres <- sprintf("%3d %3d %12.6f\n", dim(x)[1], dim(x)[2], crit) + lpad <- lname-nchar(xname) + cat(pad.right(xname,lpad), xres) + + dist <- getDistance(mm) + quantiel <- qchisq(0.975, p) + ibad <- which(dist >= quantiel) + names(ibad) <- NULL + nbad <- length(ibad) + cat("Outliers: ",nbad,"\n") + if(nbad > 0) + print(ibad) + cat("-------------\n") + show(mm) + cat("--------------------------------------------------------\n") + } + + options(digits = 5) + set.seed(101) # <<-- sub-sampling algorithm now based on R's RNG and seed + + data(heart) + data(starsCYG) + data(phosphor) + data(stackloss) + data(coleman) + data(salinity) + data(wood) + data(hbk) + + data(Animals, package = "MASS") + brain <- Animals[c(1:24, 26:25, 27:28),] + data(milk) + data(bushfire) + ### + data(rice) + data(hemophilia) + data(fish) + + tmp <- sys.call() + cat("\nCall: ", deparse(substitute(tmp)),"\n") + + cat("Data Set n p LOG(det) Time\n") + cat("===================================================\n") + doest(heart[, 1:2], data(heart), nrep, method=method) + doest(starsCYG, data(starsCYG), nrep, method=method) + doest(data.matrix(subset(phosphor, select = -plant)), data(phosphor), nrep, method=method) + doest(stack.x, data(stackloss), nrep, method=method) + doest(data.matrix(subset(coleman, select = -Y)), data(coleman), nrep, method=method) + doest(data.matrix(subset(salinity, select = -Y)), data(salinity), nrep, method=method) + doest(data.matrix(subset(wood, select = -y)), data(wood), nrep, method=method) + doest(data.matrix(subset(hbk, select = -Y)), data(hbk), nrep, method=method) + + + doest(brain, "Animals", nrep, method=method) + doest(milk, data(milk), nrep, method=method) + doest(bushfire, data(bushfire), nrep, method=method) + + doest(data.matrix(subset(rice, select = -Overall_evaluation)), data(rice), nrep, method=method) + doest(data.matrix(subset(hemophilia, select = -gr)), data(hemophilia), nrep, method=method) + doest(data.matrix(subset(fish, select = -Species)), data(fish), nrep, method=method) + + ## from package 'datasets' + doest(airquality[,1:4], data(airquality), nrep, method=method) + doest(attitude, data(attitude), nrep, method=method) + doest(attenu, data(attenu), nrep, method=method) + doest(USJudgeRatings, data(USJudgeRatings), nrep, method=method) + doest(USArrests, data(USArrests), nrep, method=method) + doest(longley, data(longley), nrep, method=method) + doest(Loblolly, data(Loblolly), nrep, method=method) + doest(quakes[,1:4], data(quakes), nrep, method=method) + + cat("===================================================\n") + } > > # generate contaminated data using the function gendata with different > # number of outliers and check if the M-estimate breaks - i.e. the > # largest eigenvalue is larger than e.g. 5. > # For n=50 and p=10 and d=5 the M-estimate can break for number of > # outliers grater than 20. > dogen <- function(){ + eig <- vector("numeric",26) + for(i in 0:25) { + gg <- gendata(eps=i) + mm <- CovSRocke(gg$x, t0=gg$tgood, S0=gg$sgood) + eig[i+1] <- ev <- getEvals(mm)[1] + cat(i, ev, "\n") + + ## stopifnot(ev < 5 || i > 20) + } + plot(0:25, eig, type="l", xlab="Number of outliers", ylab="Largest Eigenvalue") + } > > # > # generate data 50x10 as multivariate normal N(0,I) and add > # eps % outliers by adding d=5.0 to each component. > # - if eps <0 and eps <=0.5, the number of outliers is eps*n > # - if eps >= 1, it is the number of outliers > # - use the center and cov of the good data as good start > # - use the center and the cov of all data as a bad start > # If using a good start, the M-estimate must iterate to > # the good solution: the largest eigenvalue is less then e.g. 5 > # > gendata <- function(n=50, p=10, eps=0, d=5.0){ + + if(eps < 0 || eps > 0.5 && eps < 1.0 || eps > 0.5*n) + stop("eps is out of range") + + library(MASS) + + x <- mvrnorm(n, rep(0,p), diag(p)) + bad <- vector("numeric") + nbad = if(eps < 1) eps*n else eps + if(nbad > 0){ + bad <- sample(n, nbad) + x[bad,] <- x[bad,] + d + } + cov1 <- cov.wt(x) + cov2 <- if(nbad <= 0) cov1 else cov.wt(x[-bad,]) + + list(x=x, bad=sort(bad), tgood=cov2$center, sgood=cov2$cov, tbad=cov1$center, sbad=cov1$cov) + } > > pad.right <- function(z, pads) + { + ## Pads spaces to right of text + padding <- paste(rep(" ", pads), collapse = "") + paste(z, padding, sep = "") + } > > > ## -- now do it: > dodata(method="sfast") Call: dodata(method = "sfast") Data Set n p LOG(det) Time =================================================== heart 12 2 2.017701 Outliers: 3 [1] 2 6 12 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] 36.1 29.5 Robust Estimate of Covariance: height weight height 129 210 weight 210 365 -------------------------------------------------------- starsCYG 47 2 -1.450032 Outliers: 7 [1] 7 9 11 14 20 30 34 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] 4.42 4.97 Robust Estimate of Covariance: log.Te log.light log.Te 0.0176 0.0617 log.light 0.0617 0.3880 -------------------------------------------------------- phosphor 18 2 2.320721 Outliers: 2 [1] 1 6 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] 14.1 38.8 Robust Estimate of Covariance: inorg organic inorg 174 190 organic 190 268 -------------------------------------------------------- stackloss 21 3 1.470031 Outliers: 3 [1] 1 2 3 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] 57.5 20.5 86.0 Robust Estimate of Covariance: Air.Flow Water.Temp Acid.Conc. Air.Flow 38.94 11.66 22.89 Water.Temp 11.66 9.96 7.81 Acid.Conc. 22.89 7.81 40.48 -------------------------------------------------------- coleman 20 5 0.491419 Outliers: 2 [1] 6 10 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] 2.77 45.58 4.13 25.13 6.39 Robust Estimate of Covariance: salaryP fatherWc sstatus teacherSc motherLev salaryP 0.2209 1.9568 1.4389 0.2638 0.0674 fatherWc 1.9568 940.7409 307.8297 8.3290 21.9143 sstatus 1.4389 307.8297 134.0540 4.1808 7.4799 teacherSc 0.2638 8.3290 4.1808 0.7604 0.2917 motherLev 0.0674 21.9143 7.4799 0.2917 0.5817 -------------------------------------------------------- salinity 28 3 0.734619 Outliers: 4 [1] 5 16 23 24 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] 10.31 3.07 22.60 Robust Estimate of Covariance: X1 X2 X3 X1 13.200 0.784 -3.611 X2 0.784 4.441 -1.658 X3 -3.611 -1.658 2.877 -------------------------------------------------------- wood 20 5 -3.202636 Outliers: 2 [1] 7 9 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] 0.551 0.135 0.496 0.511 0.916 Robust Estimate of Covariance: x1 x2 x3 x4 x5 x1 0.011361 -0.000791 0.005473 0.004204 -0.004747 x2 -0.000791 0.000701 -0.000534 -0.001452 0.000864 x3 0.005473 -0.000534 0.004905 0.002960 -0.001914 x4 0.004204 -0.001452 0.002960 0.005154 -0.002187 x5 -0.004747 0.000864 -0.001914 -0.002187 0.003214 -------------------------------------------------------- hbk 75 3 0.283145 Outliers: 14 [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] 1.53 1.83 1.66 Robust Estimate of Covariance: X1 X2 X3 X1 1.8091 0.0479 0.2446 X2 0.0479 1.8190 0.2513 X3 0.2446 0.2513 1.7288 -------------------------------------------------------- Animals 28 2 4.685129 Outliers: 10 [1] 2 6 7 9 12 14 15 16 24 25 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] 30.8 84.2 Robust Estimate of Covariance: body brain body 14806 28767 brain 28767 65195 -------------------------------------------------------- milk 86 8 -1.437863 Outliers: 15 [1] 1 2 3 12 13 14 15 16 17 41 44 47 70 74 75 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] 1.03 35.81 32.97 26.04 25.02 24.94 122.81 14.36 Robust Estimate of Covariance: X1 X2 X3 X4 X5 X6 X7 X1 8.30e-07 2.53e-04 4.43e-04 4.02e-04 3.92e-04 3.96e-04 1.44e-03 X2 2.53e-04 2.24e+00 4.77e-01 3.63e-01 2.91e-01 3.94e-01 2.44e+00 X3 4.43e-04 4.77e-01 1.58e+00 1.20e+00 1.18e+00 1.19e+00 1.65e+00 X4 4.02e-04 3.63e-01 1.20e+00 9.74e-01 9.37e-01 9.39e-01 1.39e+00 X5 3.92e-04 2.91e-01 1.18e+00 9.37e-01 9.78e-01 9.44e-01 1.37e+00 X6 3.96e-04 3.94e-01 1.19e+00 9.39e-01 9.44e-01 9.82e-01 1.41e+00 X7 1.44e-03 2.44e+00 1.65e+00 1.39e+00 1.37e+00 1.41e+00 6.96e+00 X8 7.45e-05 3.33e-01 2.82e-01 2.01e-01 1.80e-01 1.91e-01 6.38e-01 X8 X1 7.45e-05 X2 3.33e-01 X3 2.82e-01 X4 2.01e-01 X5 1.80e-01 X6 1.91e-01 X7 6.38e-01 X8 2.01e-01 -------------------------------------------------------- bushfire 38 5 2.443148 Outliers: 13 [1] 7 8 9 10 11 31 32 33 34 35 36 37 38 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] 108 149 266 216 278 Robust Estimate of Covariance: V1 V2 V3 V4 V5 V1 911 688 -3961 -856 -707 V2 688 587 -2493 -492 -420 V3 -3961 -2493 24146 5765 4627 V4 -856 -492 5765 1477 1164 V5 -707 -420 4627 1164 925 -------------------------------------------------------- rice 105 5 -0.724874 Outliers: 7 [1] 9 40 42 49 57 58 71 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] -0.2472 0.1211 -0.1207 0.0715 0.0640 Robust Estimate of Covariance: Favor Appearance Taste Stickiness Toughness Favor 0.423 0.345 0.427 0.405 -0.202 Appearance 0.345 0.592 0.570 0.549 -0.316 Taste 0.427 0.570 0.739 0.706 -0.393 Stickiness 0.405 0.549 0.706 0.876 -0.497 Toughness -0.202 -0.316 -0.393 -0.497 0.467 -------------------------------------------------------- hemophilia 75 2 -1.868949 Outliers: 2 [1] 11 36 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] -0.2126 -0.0357 Robust Estimate of Covariance: AHFactivity AHFantigen AHFactivity 0.0317 0.0112 AHFantigen 0.0112 0.0218 -------------------------------------------------------- fish 159 6 1.285876 Outliers: 21 [1] 61 62 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 [20] 103 142 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] 358.3 24.7 26.9 29.7 30.0 14.7 Robust Estimate of Covariance: Weight Length1 Length2 Length3 Height Width Weight 1.33e+05 3.09e+03 3.34e+03 3.78e+03 1.72e+03 2.24e+02 Length1 3.09e+03 7.92e+01 8.54e+01 9.55e+01 4.04e+01 7.43e+00 Length2 3.34e+03 8.54e+01 9.22e+01 1.03e+02 4.49e+01 8.07e+00 Length3 3.78e+03 9.55e+01 1.03e+02 1.18e+02 5.92e+01 7.65e+00 Height 1.72e+03 4.04e+01 4.49e+01 5.92e+01 7.12e+01 8.51e-01 Width 2.24e+02 7.43e+00 8.07e+00 7.65e+00 8.51e-01 3.57e+00 -------------------------------------------------------- airquality 153 4 2.684374 Outliers: 7 [1] 7 14 23 30 34 77 107 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] 39.34 192.12 9.67 78.71 Robust Estimate of Covariance: Ozone Solar.R Wind Temp Ozone 973.104 894.011 -61.856 243.560 Solar.R 894.011 9677.269 0.388 179.429 Wind -61.856 0.388 11.287 -14.310 Temp 243.560 179.429 -14.310 96.714 -------------------------------------------------------- attitude 30 7 2.091968 Outliers: 4 [1] 14 16 18 24 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] 65.7 66.8 51.9 56.1 66.4 76.7 43.0 Robust Estimate of Covariance: rating complaints privileges learning raises critical advance rating 170.59 136.40 77.41 125.46 99.72 8.01 49.52 complaints 136.40 170.94 94.62 136.73 120.76 23.52 78.52 privileges 77.41 94.62 150.49 112.77 87.92 6.43 72.33 learning 125.46 136.73 112.77 173.77 131.46 25.81 81.38 raises 99.72 120.76 87.92 131.46 136.76 29.50 91.70 critical 8.01 23.52 6.43 25.81 29.50 84.75 30.59 advance 49.52 78.52 72.33 81.38 91.70 30.59 116.28 -------------------------------------------------------- attenu 182 5 1.148032 Outliers: 31 [1] 2 5 6 7 8 9 10 11 15 16 19 20 21 22 23 24 25 27 28 [20] 29 30 31 32 64 65 80 94 95 96 97 100 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] 16.432 5.849 60.297 27.144 0.134 Robust Estimate of Covariance: event mag station dist accel event 54.9236 -3.0733 181.0954 -49.4194 -0.0628 mag -3.0733 0.6530 -8.4388 6.7388 0.0161 station 181.0954 -8.4388 1689.7161 -114.6319 0.7285 dist -49.4194 6.7388 -114.6319 597.3606 -1.7988 accel -0.0628 0.0161 0.7285 -1.7988 0.0152 -------------------------------------------------------- USJudgeRatings 43 12 -1.683847 Outliers: 7 [1] 5 7 12 13 14 23 31 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] 7.43 8.16 7.75 7.89 7.68 7.76 7.67 7.67 7.51 7.58 8.19 7.86 Robust Estimate of Covariance: CONT INTG DMNR DILG CFMG DECI PREP FAMI CONT 0.8710 -0.3019 -0.4682 -0.1893 -0.0569 -0.0992 -0.1771 -0.1975 INTG -0.3019 0.6401 0.8598 0.6955 0.5732 0.5439 0.7091 0.7084 DMNR -0.4682 0.8598 1.2412 0.9107 0.7668 0.7305 0.9292 0.9158 DILG -0.1893 0.6955 0.9107 0.8554 0.7408 0.7036 0.8865 0.8791 CFMG -0.0569 0.5732 0.7668 0.7408 0.6994 0.6545 0.7788 0.7721 DECI -0.0992 0.5439 0.7305 0.7036 0.6545 0.6342 0.7492 0.7511 PREP -0.1771 0.7091 0.9292 0.8865 0.7788 0.7492 0.9541 0.9556 FAMI -0.1975 0.7084 0.9158 0.8791 0.7721 0.7511 0.9556 0.9785 ORAL -0.2444 0.7453 0.9939 0.8917 0.7842 0.7551 0.9554 0.9680 WRIT -0.2344 0.7319 0.9649 0.8853 0.7781 0.7511 0.9498 0.9668 PHYS -0.1983 0.4676 0.6263 0.5629 0.5073 0.5039 0.5990 0.6140 RTEN -0.3152 0.8000 1.0798 0.9234 0.7952 0.7663 0.9637 0.9693 ORAL WRIT PHYS RTEN CONT -0.2444 -0.2344 -0.1983 -0.3152 INTG 0.7453 0.7319 0.4676 0.8000 DMNR 0.9939 0.9649 0.6263 1.0798 DILG 0.8917 0.8853 0.5629 0.9234 CFMG 0.7842 0.7781 0.5073 0.7952 DECI 0.7551 0.7511 0.5039 0.7663 PREP 0.9554 0.9498 0.5990 0.9637 FAMI 0.9680 0.9668 0.6140 0.9693 ORAL 0.9853 0.9744 0.6280 1.0032 WRIT 0.9744 0.9711 0.6184 0.9870 PHYS 0.6280 0.6184 0.4716 0.6520 RTEN 1.0032 0.9870 0.6520 1.0622 -------------------------------------------------------- USArrests 50 4 2.411726 Outliers: 4 [1] 2 28 33 39 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] 7.05 150.66 64.66 19.37 Robust Estimate of Covariance: Murder Assault UrbanPop Rape Murder 23.8 380.8 19.2 29.7 Assault 380.8 8436.2 605.6 645.3 UrbanPop 19.2 605.6 246.5 78.8 Rape 29.7 645.3 78.8 77.3 -------------------------------------------------------- longley 16 7 1.038316 Outliers: 5 [1] 1 2 3 4 5 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] 107.6 440.8 339.7 292.5 121.0 1957.1 67.2 Robust Estimate of Covariance: GNP.deflator GNP Unemployed Armed.Forces Population GNP.deflator 100.6 954.7 1147.1 -507.6 74.2 GNP 954.7 9430.9 10115.8 -4616.5 730.1 Unemployed 1147.1 10115.8 19838.3 -6376.9 850.6 Armed.Forces -507.6 -4616.5 -6376.9 3240.2 -351.3 Population 74.2 730.1 850.6 -351.3 57.5 Year 46.4 450.8 539.5 -233.0 35.3 Employed 30.8 310.5 274.0 -160.8 23.3 Year Employed GNP.deflator 46.4 30.8 GNP 450.8 310.5 Unemployed 539.5 274.0 Armed.Forces -233.0 -160.8 Population 35.3 23.3 Year 21.9 14.6 Employed 14.6 11.2 -------------------------------------------------------- Loblolly 84 3 1.481317 Outliers: 14 [1] 6 12 18 24 30 36 42 48 54 60 66 72 78 84 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] 24.22 9.65 7.50 Robust Estimate of Covariance: height age Seed height 525.08 179.21 14.27 age 179.21 61.85 2.94 Seed 14.27 2.94 25.86 -------------------------------------------------------- quakes 1000 4 1.576855 Outliers: 223 [1] 7 12 15 17 22 25 27 28 32 37 40 41 45 48 53 [16] 63 64 73 78 87 91 92 94 99 108 110 117 118 119 120 [31] 121 122 126 133 136 141 143 145 148 152 154 155 157 159 160 [46] 163 170 192 205 222 226 230 239 243 250 251 252 254 258 263 [61] 267 268 271 283 292 300 301 305 311 312 318 320 321 325 328 [76] 330 334 352 357 360 365 381 382 384 389 400 402 408 413 416 [91] 417 419 426 429 437 441 443 453 456 467 474 477 490 492 496 [106] 504 507 508 509 517 524 527 528 531 532 534 536 538 539 541 [121] 542 543 544 545 546 547 552 553 560 571 581 583 587 593 594 [136] 596 597 605 612 613 618 620 625 629 638 642 647 649 653 655 [151] 656 672 675 681 686 699 701 702 712 714 716 721 725 726 735 [166] 744 754 756 759 765 766 769 779 781 782 785 787 797 804 813 [181] 825 827 837 840 844 852 853 857 860 865 866 869 870 872 873 [196] 883 884 887 888 890 891 893 908 909 912 915 916 921 927 930 [211] 952 962 963 969 974 980 982 986 987 988 992 997 1000 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: S-FAST Robust Estimate of Location: [1] -21.54 182.35 369.21 4.54 Robust Estimate of Covariance: lat long depth mag lat 2.81e+01 6.19e+00 3.27e+02 -4.56e-01 long 6.19e+00 7.54e+00 -5.95e+02 9.56e-02 depth 3.27e+02 -5.95e+02 8.36e+04 -2.70e+01 mag -4.56e-01 9.56e-02 -2.70e+01 2.35e-01 -------------------------------------------------------- =================================================== > dodata(method="sdet") Call: dodata(method = "sdet") Data Set n p LOG(det) Time =================================================== heart 12 2 2.017701 Outliers: 3 [1] 2 6 12 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] 36.1 29.5 Robust Estimate of Covariance: height weight height 129 210 weight 210 365 -------------------------------------------------------- starsCYG 47 2 -1.450032 Outliers: 7 [1] 7 9 11 14 20 30 34 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] 4.42 4.97 Robust Estimate of Covariance: log.Te log.light log.Te 0.0176 0.0617 log.light 0.0617 0.3880 -------------------------------------------------------- phosphor 18 2 2.320721 Outliers: 2 [1] 1 6 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] 14.1 38.8 Robust Estimate of Covariance: inorg organic inorg 174 190 organic 190 268 -------------------------------------------------------- stackloss 21 3 1.470031 Outliers: 3 [1] 1 2 3 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] 57.5 20.5 86.0 Robust Estimate of Covariance: Air.Flow Water.Temp Acid.Conc. Air.Flow 38.94 11.66 22.89 Water.Temp 11.66 9.96 7.81 Acid.Conc. 22.89 7.81 40.48 -------------------------------------------------------- coleman 20 5 0.491419 Outliers: 2 [1] 6 10 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] 2.77 45.58 4.13 25.13 6.39 Robust Estimate of Covariance: salaryP fatherWc sstatus teacherSc motherLev salaryP 0.2209 1.9568 1.4389 0.2638 0.0674 fatherWc 1.9568 940.7409 307.8297 8.3290 21.9143 sstatus 1.4389 307.8297 134.0540 4.1808 7.4799 teacherSc 0.2638 8.3290 4.1808 0.7604 0.2917 motherLev 0.0674 21.9143 7.4799 0.2917 0.5817 -------------------------------------------------------- salinity 28 3 0.734619 Outliers: 4 [1] 5 16 23 24 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] 10.31 3.07 22.60 Robust Estimate of Covariance: X1 X2 X3 X1 13.200 0.784 -3.611 X2 0.784 4.441 -1.658 X3 -3.611 -1.658 2.877 -------------------------------------------------------- wood 20 5 -3.220754 Outliers: 4 [1] 4 6 8 19 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] 0.580 0.123 0.530 0.538 0.890 Robust Estimate of Covariance: x1 x2 x3 x4 x5 x1 8.16e-03 1.39e-03 1.97e-03 -2.82e-04 -7.61e-04 x2 1.39e-03 4.00e-04 8.14e-04 -8.51e-05 -5.07e-06 x3 1.97e-03 8.14e-04 4.74e-03 -9.59e-04 2.06e-05 x4 -2.82e-04 -8.51e-05 -9.59e-04 3.09e-03 1.87e-03 x5 -7.61e-04 -5.07e-06 2.06e-05 1.87e-03 2.28e-03 -------------------------------------------------------- hbk 75 3 0.283145 Outliers: 14 [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] 1.53 1.83 1.66 Robust Estimate of Covariance: X1 X2 X3 X1 1.8091 0.0479 0.2446 X2 0.0479 1.8190 0.2513 X3 0.2446 0.2513 1.7288 -------------------------------------------------------- Animals 28 2 4.685129 Outliers: 10 [1] 2 6 7 9 12 14 15 16 24 25 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] 30.8 84.2 Robust Estimate of Covariance: body brain body 14806 28767 brain 28767 65194 -------------------------------------------------------- milk 86 8 -1.437863 Outliers: 15 [1] 1 2 3 12 13 14 15 16 17 41 44 47 70 74 75 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] 1.03 35.81 32.97 26.04 25.02 24.94 122.81 14.36 Robust Estimate of Covariance: X1 X2 X3 X4 X5 X6 X7 X1 8.30e-07 2.53e-04 4.43e-04 4.02e-04 3.92e-04 3.96e-04 1.44e-03 X2 2.53e-04 2.24e+00 4.77e-01 3.63e-01 2.91e-01 3.94e-01 2.44e+00 X3 4.43e-04 4.77e-01 1.58e+00 1.20e+00 1.18e+00 1.19e+00 1.65e+00 X4 4.02e-04 3.63e-01 1.20e+00 9.74e-01 9.37e-01 9.39e-01 1.39e+00 X5 3.92e-04 2.91e-01 1.18e+00 9.37e-01 9.78e-01 9.44e-01 1.37e+00 X6 3.96e-04 3.94e-01 1.19e+00 9.39e-01 9.44e-01 9.82e-01 1.41e+00 X7 1.44e-03 2.44e+00 1.65e+00 1.39e+00 1.37e+00 1.41e+00 6.96e+00 X8 7.45e-05 3.33e-01 2.82e-01 2.01e-01 1.80e-01 1.91e-01 6.38e-01 X8 X1 7.45e-05 X2 3.33e-01 X3 2.82e-01 X4 2.01e-01 X5 1.80e-01 X6 1.91e-01 X7 6.38e-01 X8 2.01e-01 -------------------------------------------------------- bushfire 38 5 2.443148 Outliers: 13 [1] 7 8 9 10 11 31 32 33 34 35 36 37 38 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] 108 149 266 216 278 Robust Estimate of Covariance: V1 V2 V3 V4 V5 V1 911 688 -3961 -856 -707 V2 688 587 -2493 -492 -420 V3 -3961 -2493 24146 5765 4627 V4 -856 -492 5765 1477 1164 V5 -707 -420 4627 1164 925 -------------------------------------------------------- rice 105 5 -0.724874 Outliers: 7 [1] 9 40 42 49 57 58 71 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] -0.2472 0.1211 -0.1207 0.0715 0.0640 Robust Estimate of Covariance: Favor Appearance Taste Stickiness Toughness Favor 0.423 0.345 0.427 0.405 -0.202 Appearance 0.345 0.592 0.570 0.549 -0.316 Taste 0.427 0.570 0.739 0.706 -0.393 Stickiness 0.405 0.549 0.706 0.876 -0.497 Toughness -0.202 -0.316 -0.393 -0.497 0.467 -------------------------------------------------------- hemophilia 75 2 -1.868949 Outliers: 2 [1] 11 36 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] -0.2126 -0.0357 Robust Estimate of Covariance: AHFactivity AHFantigen AHFactivity 0.0317 0.0112 AHFantigen 0.0112 0.0218 -------------------------------------------------------- fish 159 6 1.267294 Outliers: 33 [1] 61 72 73 74 75 76 77 78 79 80 81 82 83 85 86 87 88 89 90 [20] 91 92 93 94 95 96 97 98 99 100 101 102 103 142 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] 381.2 25.6 27.8 30.8 31.0 14.9 Robust Estimate of Covariance: Weight Length1 Length2 Length3 Height Width Weight 148372.04 3260.48 3508.71 3976.93 1507.43 127.94 Length1 3260.48 77.00 82.52 92.18 27.56 3.29 Length2 3508.71 82.52 88.57 99.20 30.83 3.43 Length3 3976.93 92.18 99.20 113.97 45.50 2.21 Height 1507.43 27.56 30.83 45.50 70.54 -4.95 Width 127.94 3.29 3.43 2.21 -4.95 2.28 -------------------------------------------------------- airquality 153 4 2.684374 Outliers: 7 [1] 7 14 23 30 34 77 107 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] 39.34 192.12 9.67 78.71 Robust Estimate of Covariance: Ozone Solar.R Wind Temp Ozone 973.104 894.011 -61.856 243.560 Solar.R 894.011 9677.269 0.388 179.429 Wind -61.856 0.388 11.287 -14.310 Temp 243.560 179.429 -14.310 96.714 -------------------------------------------------------- attitude 30 7 2.091968 Outliers: 4 [1] 14 16 18 24 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] 65.7 66.8 51.9 56.1 66.4 76.7 43.0 Robust Estimate of Covariance: rating complaints privileges learning raises critical advance rating 170.59 136.40 77.41 125.46 99.72 8.01 49.52 complaints 136.40 170.94 94.62 136.73 120.76 23.52 78.52 privileges 77.41 94.62 150.49 112.77 87.92 6.43 72.33 learning 125.46 136.73 112.77 173.77 131.46 25.81 81.38 raises 99.72 120.76 87.92 131.46 136.76 29.50 91.70 critical 8.01 23.52 6.43 25.81 29.50 84.75 30.59 advance 49.52 78.52 72.33 81.38 91.70 30.59 116.28 -------------------------------------------------------- attenu 182 5 1.148032 Outliers: 31 [1] 2 5 6 7 8 9 10 11 15 16 19 20 21 22 23 24 25 27 28 [20] 29 30 31 32 64 65 80 94 95 96 97 100 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] 16.432 5.849 60.297 27.144 0.134 Robust Estimate of Covariance: event mag station dist accel event 54.9236 -3.0733 181.0954 -49.4195 -0.0628 mag -3.0733 0.6530 -8.4388 6.7388 0.0161 station 181.0954 -8.4388 1689.7161 -114.6321 0.7285 dist -49.4195 6.7388 -114.6321 597.3609 -1.7988 accel -0.0628 0.0161 0.7285 -1.7988 0.0152 -------------------------------------------------------- USJudgeRatings 43 12 -1.683847 Outliers: 7 [1] 5 7 12 13 14 23 31 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] 7.43 8.16 7.75 7.89 7.68 7.76 7.67 7.67 7.51 7.58 8.19 7.86 Robust Estimate of Covariance: CONT INTG DMNR DILG CFMG DECI PREP FAMI CONT 0.8715 -0.3020 -0.4683 -0.1894 -0.0569 -0.0993 -0.1772 -0.1976 INTG -0.3020 0.6403 0.8600 0.6956 0.5733 0.5440 0.7093 0.7086 DMNR -0.4683 0.8600 1.2416 0.9109 0.7669 0.7307 0.9295 0.9161 DILG -0.1894 0.6956 0.9109 0.8555 0.7410 0.7037 0.8867 0.8793 CFMG -0.0569 0.5733 0.7669 0.7410 0.6995 0.6546 0.7789 0.7723 DECI -0.0993 0.5440 0.7307 0.7037 0.6546 0.6343 0.7493 0.7513 PREP -0.1772 0.7093 0.9295 0.8867 0.7789 0.7493 0.9543 0.9559 FAMI -0.1976 0.7086 0.9161 0.8793 0.7723 0.7513 0.9559 0.9788 ORAL -0.2445 0.7456 0.9942 0.8919 0.7844 0.7553 0.9557 0.9683 WRIT -0.2345 0.7321 0.9652 0.8856 0.7783 0.7513 0.9501 0.9671 PHYS -0.1986 0.4676 0.6264 0.5628 0.5072 0.5038 0.5990 0.6140 RTEN -0.3154 0.8002 1.0801 0.9236 0.7954 0.7665 0.9639 0.9695 ORAL WRIT PHYS RTEN CONT -0.2445 -0.2345 -0.1986 -0.3154 INTG 0.7456 0.7321 0.4676 0.8002 DMNR 0.9942 0.9652 0.6264 1.0801 DILG 0.8919 0.8856 0.5628 0.9236 CFMG 0.7844 0.7783 0.5072 0.7954 DECI 0.7553 0.7513 0.5038 0.7665 PREP 0.9557 0.9501 0.5990 0.9639 FAMI 0.9683 0.9671 0.6140 0.9695 ORAL 0.9856 0.9748 0.6281 1.0035 WRIT 0.9748 0.9714 0.6184 0.9873 PHYS 0.6281 0.6184 0.4713 0.6520 RTEN 1.0035 0.9873 0.6520 1.0624 -------------------------------------------------------- USArrests 50 4 2.411726 Outliers: 4 [1] 2 28 33 39 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] 7.05 150.66 64.66 19.37 Robust Estimate of Covariance: Murder Assault UrbanPop Rape Murder 23.8 380.8 19.2 29.7 Assault 380.8 8436.2 605.6 645.3 UrbanPop 19.2 605.6 246.5 78.8 Rape 29.7 645.3 78.8 77.3 -------------------------------------------------------- longley 16 7 1.143113 Outliers: 4 [1] 1 2 3 4 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] 107 435 334 293 120 1957 67 Robust Estimate of Covariance: GNP.deflator GNP Unemployed Armed.Forces Population GNP.deflator 89.2 850.1 1007.4 -404.4 66.2 GNP 850.1 8384.4 9020.8 -3692.0 650.5 Unemployed 1007.4 9020.8 16585.4 -4990.7 752.5 Armed.Forces -404.4 -3692.0 -4990.7 2474.2 -280.9 Population 66.2 650.5 752.5 -280.9 51.2 Year 41.9 407.6 481.9 -186.4 31.9 Employed 27.9 279.7 255.6 -128.8 21.1 Year Employed GNP.deflator 41.9 27.9 GNP 407.6 279.7 Unemployed 481.9 255.6 Armed.Forces -186.4 -128.8 Population 31.9 21.1 Year 20.2 13.4 Employed 13.4 10.1 -------------------------------------------------------- Loblolly 84 3 1.481317 Outliers: 14 [1] 6 12 18 24 30 36 42 48 54 60 66 72 78 84 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] 24.22 9.65 7.50 Robust Estimate of Covariance: height age Seed height 525.08 179.21 14.27 age 179.21 61.85 2.94 Seed 14.27 2.94 25.86 -------------------------------------------------------- quakes 1000 4 1.576855 Outliers: 223 [1] 7 12 15 17 22 25 27 28 32 37 40 41 45 48 53 [16] 63 64 73 78 87 91 92 94 99 108 110 117 118 119 120 [31] 121 122 126 133 136 141 143 145 148 152 154 155 157 159 160 [46] 163 170 192 205 222 226 230 239 243 250 251 252 254 258 263 [61] 267 268 271 283 292 300 301 305 311 312 318 320 321 325 328 [76] 330 334 352 357 360 365 381 382 384 389 400 402 408 413 416 [91] 417 419 426 429 437 441 443 453 456 467 474 477 490 492 496 [106] 504 507 508 509 517 524 527 528 531 532 534 536 538 539 541 [121] 542 543 544 545 546 547 552 553 560 571 581 583 587 593 594 [136] 596 597 605 612 613 618 620 625 629 638 642 647 649 653 655 [151] 656 672 675 681 686 699 701 702 712 714 716 721 725 726 735 [166] 744 754 756 759 765 766 769 779 781 782 785 787 797 804 813 [181] 825 827 837 840 844 852 853 857 860 865 866 869 870 872 873 [196] 883 884 887 888 890 891 893 908 909 912 915 916 921 927 930 [211] 952 962 963 969 974 980 982 986 987 988 992 997 1000 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: DET-S Robust Estimate of Location: [1] -21.54 182.35 369.21 4.54 Robust Estimate of Covariance: lat long depth mag lat 2.81e+01 6.19e+00 3.27e+02 -4.56e-01 long 6.19e+00 7.54e+00 -5.95e+02 9.56e-02 depth 3.27e+02 -5.95e+02 8.36e+04 -2.70e+01 mag -4.56e-01 9.56e-02 -2.70e+01 2.35e-01 -------------------------------------------------------- =================================================== > ##dodata(method="suser") > ##dodata(method="surreal") > dodata(method="bisquare") Call: dodata(method = "bisquare") Data Set n p LOG(det) Time =================================================== heart 12 2 7.721793 Outliers: 3 [1] 2 6 12 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: height weight 36.1 29.4 Robust Estimate of Covariance: height weight height 109 177 weight 177 307 -------------------------------------------------------- starsCYG 47 2 -5.942108 Outliers: 7 [1] 7 9 11 14 20 30 34 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: log.Te log.light 4.42 4.97 Robust Estimate of Covariance: log.Te log.light log.Te 0.0164 0.0574 log.light 0.0574 0.3613 -------------------------------------------------------- phosphor 18 2 9.269096 Outliers: 2 [1] 1 6 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: inorg organic 14.1 38.7 Robust Estimate of Covariance: inorg organic inorg 173 189 organic 189 268 -------------------------------------------------------- stackloss 21 3 8.411100 Outliers: 3 [1] 1 2 3 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: Air.Flow Water.Temp Acid.Conc. 57.5 20.5 86.0 Robust Estimate of Covariance: Air.Flow Water.Temp Acid.Conc. Air.Flow 33.82 10.17 20.02 Water.Temp 10.17 8.70 6.84 Acid.Conc. 20.02 6.84 35.51 -------------------------------------------------------- coleman 20 5 4.722046 Outliers: 2 [1] 6 10 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: salaryP fatherWc sstatus teacherSc motherLev 2.77 45.59 4.14 25.13 6.39 Robust Estimate of Covariance: salaryP fatherWc sstatus teacherSc motherLev salaryP 0.2135 1.8732 1.3883 0.2547 0.0648 fatherWc 1.8732 905.6704 296.1916 7.9820 21.0848 sstatus 1.3883 296.1916 128.9536 4.0196 7.1917 teacherSc 0.2547 7.9820 4.0196 0.7321 0.2799 motherLev 0.0648 21.0848 7.1917 0.2799 0.5592 -------------------------------------------------------- salinity 28 3 4.169963 Outliers: 4 [1] 5 16 23 24 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: X1 X2 X3 10.30 3.07 22.59 Robust Estimate of Covariance: X1 X2 X3 X1 12.234 0.748 -3.369 X2 0.748 4.115 -1.524 X3 -3.369 -1.524 2.655 -------------------------------------------------------- wood 20 5 -33.862485 Outliers: 5 [1] 4 6 8 11 19 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: x1 x2 x3 x4 x5 0.580 0.123 0.530 0.538 0.890 Robust Estimate of Covariance: x1 x2 x3 x4 x5 x1 5.88e-03 9.96e-04 1.43e-03 -1.96e-04 -5.46e-04 x2 9.96e-04 2.86e-04 5.89e-04 -5.78e-05 -2.24e-06 x3 1.43e-03 5.89e-04 3.42e-03 -6.95e-04 1.43e-05 x4 -1.96e-04 -5.78e-05 -6.95e-04 2.23e-03 1.35e-03 x5 -5.46e-04 -2.24e-06 1.43e-05 1.35e-03 1.65e-03 -------------------------------------------------------- hbk 75 3 1.472421 Outliers: 14 [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: X1 X2 X3 1.53 1.83 1.66 Robust Estimate of Covariance: X1 X2 X3 X1 1.6775 0.0447 0.2268 X2 0.0447 1.6865 0.2325 X3 0.2268 0.2325 1.6032 -------------------------------------------------------- Animals 28 2 18.528307 Outliers: 11 [1] 2 6 7 9 12 14 15 16 24 25 28 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: body brain 30.7 84.1 Robust Estimate of Covariance: body brain body 13278 25795 brain 25795 58499 -------------------------------------------------------- milk 86 8 -24.816943 Outliers: 19 [1] 1 2 3 11 12 13 14 15 16 17 20 27 41 44 47 70 74 75 77 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: X1 X2 X3 X4 X5 X6 X7 X8 1.03 35.81 32.96 26.04 25.02 24.94 122.79 14.35 Robust Estimate of Covariance: X1 X2 X3 X4 X5 X6 X7 X1 6.80e-07 2.20e-04 3.70e-04 3.35e-04 3.27e-04 3.30e-04 1.21e-03 X2 2.20e-04 1.80e+00 3.96e-01 3.03e-01 2.45e-01 3.27e-01 2.00e+00 X3 3.70e-04 3.96e-01 1.27e+00 9.68e-01 9.49e-01 9.56e-01 1.37e+00 X4 3.35e-04 3.03e-01 9.68e-01 7.86e-01 7.55e-01 7.57e-01 1.15e+00 X5 3.27e-04 2.45e-01 9.49e-01 7.55e-01 7.88e-01 7.61e-01 1.14e+00 X6 3.30e-04 3.27e-01 9.56e-01 7.57e-01 7.61e-01 7.90e-01 1.17e+00 X7 1.21e-03 2.00e+00 1.37e+00 1.15e+00 1.14e+00 1.17e+00 5.71e+00 X8 6.57e-05 2.71e-01 2.30e-01 1.64e-01 1.48e-01 1.57e-01 5.27e-01 X8 X1 6.57e-05 X2 2.71e-01 X3 2.30e-01 X4 1.64e-01 X5 1.48e-01 X6 1.57e-01 X7 5.27e-01 X8 1.62e-01 -------------------------------------------------------- bushfire 38 5 21.704243 Outliers: 13 [1] 7 8 9 10 11 31 32 33 34 35 36 37 38 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: V1 V2 V3 V4 V5 108 149 266 216 278 Robust Estimate of Covariance: V1 V2 V3 V4 V5 V1 528 398 -2298 -497 -410 V2 398 340 -1445 -285 -244 V3 -2298 -1445 14026 3348 2687 V4 -497 -285 3348 857 676 V5 -410 -244 2687 676 537 -------------------------------------------------------- rice 105 5 -7.346939 Outliers: 8 [1] 9 14 40 42 49 57 58 71 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: Favor Appearance Taste Stickiness Toughness -0.2480 0.1203 -0.1213 0.0710 0.0644 Robust Estimate of Covariance: Favor Appearance Taste Stickiness Toughness Favor 0.415 0.338 0.419 0.398 -0.198 Appearance 0.338 0.580 0.559 0.539 -0.310 Taste 0.419 0.559 0.725 0.693 -0.386 Stickiness 0.398 0.539 0.693 0.859 -0.487 Toughness -0.198 -0.310 -0.386 -0.487 0.457 -------------------------------------------------------- hemophilia 75 2 -7.465173 Outliers: 2 [1] 11 36 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: AHFactivity AHFantigen -0.2128 -0.0366 Robust Estimate of Covariance: AHFactivity AHFantigen AHFactivity 0.0321 0.0115 AHFantigen 0.0115 0.0220 -------------------------------------------------------- fish 159 6 13.465134 Outliers: 35 [1] 38 61 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 [20] 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 142 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: Weight Length1 Length2 Length3 Height Width 381.4 25.6 27.8 30.8 31.0 14.9 Robust Estimate of Covariance: Weight Length1 Length2 Length3 Height Width Weight 111094.92 2440.81 2626.59 2976.92 1129.78 95.85 Length1 2440.81 57.63 61.75 68.98 20.67 2.46 Length2 2626.59 61.75 66.28 74.24 23.13 2.57 Length3 2976.92 68.98 74.24 85.29 34.11 1.65 Height 1129.78 20.67 23.13 34.11 52.75 -3.70 Width 95.85 2.46 2.57 1.65 -3.70 1.71 -------------------------------------------------------- airquality 153 4 21.282926 Outliers: 8 [1] 7 11 14 23 30 34 77 107 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: Ozone Solar.R Wind Temp 39.40 192.29 9.66 78.74 Robust Estimate of Covariance: Ozone Solar.R Wind Temp Ozone 930.566 849.644 -59.157 232.459 Solar.R 849.644 9207.569 0.594 168.122 Wind -59.157 0.594 10.783 -13.645 Temp 232.459 168.122 -13.645 92.048 -------------------------------------------------------- attitude 30 7 28.084183 Outliers: 6 [1] 6 9 14 16 18 24 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: rating complaints privileges learning raises critical 65.7 66.8 51.9 56.1 66.4 76.7 advance 43.0 Robust Estimate of Covariance: rating complaints privileges learning raises critical advance rating 143.88 114.95 64.97 105.69 83.95 6.96 41.78 complaints 114.95 143.84 79.28 115.00 101.48 19.69 66.13 privileges 64.97 79.28 126.38 94.70 73.87 5.37 61.07 learning 105.69 115.00 94.70 146.14 110.50 21.67 68.49 raises 83.95 101.48 73.87 110.50 115.01 24.91 77.16 critical 6.96 19.69 5.37 21.67 24.91 71.74 25.88 advance 41.78 66.13 61.07 68.49 77.16 25.88 97.71 -------------------------------------------------------- attenu 182 5 10.109049 Outliers: 35 [1] 2 4 5 6 7 8 9 10 11 15 16 19 20 21 22 23 24 25 27 [20] 28 29 30 31 32 64 65 80 93 94 95 96 97 98 99 100 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: event mag station dist accel 16.418 5.850 60.243 27.307 0.134 Robust Estimate of Covariance: event mag station dist accel event 41.9000 -2.3543 137.8110 -39.0321 -0.0447 mag -2.3543 0.4978 -6.4461 5.2644 0.0118 station 137.8110 -6.4461 1283.9675 -90.1657 0.5554 dist -39.0321 5.2644 -90.1657 462.3898 -1.3672 accel -0.0447 0.0118 0.5554 -1.3672 0.0114 -------------------------------------------------------- USJudgeRatings 43 12 -43.367499 Outliers: 10 [1] 5 7 8 12 13 14 20 23 31 35 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: CONT INTG DMNR DILG CFMG DECI PREP FAMI ORAL WRIT PHYS RTEN 7.43 8.16 7.75 7.89 7.69 7.76 7.68 7.67 7.52 7.59 8.19 7.87 Robust Estimate of Covariance: CONT INTG DMNR DILG CFMG DECI PREP FAMI CONT 0.6895 -0.2399 -0.3728 -0.1514 -0.0461 -0.0801 -0.1419 -0.1577 INTG -0.2399 0.5021 0.6746 0.5446 0.4479 0.4254 0.5564 0.5558 DMNR -0.3728 0.6746 0.9753 0.7128 0.5992 0.5715 0.7289 0.7181 DILG -0.1514 0.5446 0.7128 0.6691 0.5789 0.5501 0.6949 0.6892 CFMG -0.0461 0.4479 0.5992 0.5789 0.5468 0.5118 0.6100 0.6049 DECI -0.0801 0.4254 0.5715 0.5501 0.5118 0.4965 0.5872 0.5890 PREP -0.1419 0.5564 0.7289 0.6949 0.6100 0.5872 0.7497 0.7511 FAMI -0.1577 0.5558 0.7181 0.6892 0.6049 0.5890 0.7511 0.7696 ORAL -0.1950 0.5848 0.7798 0.6990 0.6143 0.5921 0.7508 0.7610 WRIT -0.1866 0.5747 0.7575 0.6946 0.6101 0.5895 0.7470 0.7607 PHYS -0.1620 0.3640 0.4878 0.4361 0.3927 0.3910 0.4655 0.4779 RTEN -0.2522 0.6268 0.8462 0.7220 0.6210 0.5991 0.7553 0.7599 ORAL WRIT PHYS RTEN CONT -0.1950 -0.1866 -0.1620 -0.2522 INTG 0.5848 0.5747 0.3640 0.6268 DMNR 0.7798 0.7575 0.4878 0.8462 DILG 0.6990 0.6946 0.4361 0.7220 CFMG 0.6143 0.6101 0.3927 0.6210 DECI 0.5921 0.5895 0.3910 0.5991 PREP 0.7508 0.7470 0.4655 0.7553 FAMI 0.7610 0.7607 0.4779 0.7599 ORAL 0.7745 0.7665 0.4893 0.7866 WRIT 0.7665 0.7645 0.4823 0.7745 PHYS 0.4893 0.4823 0.3620 0.5062 RTEN 0.7866 0.7745 0.5062 0.8313 -------------------------------------------------------- USArrests 50 4 19.266763 Outliers: 4 [1] 2 28 33 39 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: Murder Assault UrbanPop Rape 7.04 150.55 64.64 19.34 Robust Estimate of Covariance: Murder Assault UrbanPop Rape Murder 23.7 378.9 19.1 29.5 Assault 378.9 8388.2 601.3 639.7 UrbanPop 19.1 601.3 245.3 77.9 Rape 29.5 639.7 77.9 76.3 -------------------------------------------------------- longley 16 7 13.789499 Outliers: 4 [1] 1 2 3 4 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: GNP.deflator GNP Unemployed Armed.Forces Population 107 435 333 293 120 Year Employed 1957 67 Robust Estimate of Covariance: GNP.deflator GNP Unemployed Armed.Forces Population GNP.deflator 65.05 619.75 734.33 -294.02 48.27 GNP 619.75 6112.14 6578.12 -2684.52 474.26 Unemployed 734.33 6578.12 12075.90 -3627.79 548.58 Armed.Forces -294.02 -2684.52 -3627.79 1797.05 -204.25 Population 48.27 474.26 548.58 -204.25 37.36 Year 30.58 297.29 351.44 -135.53 23.29 Employed 20.36 203.96 186.62 -93.64 15.42 Year Employed GNP.deflator 30.58 20.36 GNP 297.29 203.96 Unemployed 351.44 186.62 Armed.Forces -135.53 -93.64 Population 23.29 15.42 Year 14.70 9.80 Employed 9.80 7.36 -------------------------------------------------------- Loblolly 84 3 8.518440 Outliers: 14 [1] 6 12 18 24 30 36 42 48 54 60 66 72 78 84 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: height age Seed 24.14 9.62 7.51 Robust Estimate of Covariance: height age Seed height 464.64 158.43 12.83 age 158.43 54.62 2.67 Seed 12.83 2.67 22.98 -------------------------------------------------------- quakes 1000 4 11.611413 Outliers: 234 [1] 7 12 15 17 22 25 27 28 32 37 40 41 45 48 53 [16] 63 64 73 78 87 91 92 94 99 108 110 117 118 119 120 [31] 121 122 126 133 136 141 143 145 148 152 154 155 157 159 160 [46] 163 166 170 174 192 205 222 226 230 239 243 250 251 252 254 [61] 258 263 267 268 271 283 292 297 300 301 305 311 312 318 320 [76] 321 325 328 330 331 334 352 357 360 365 368 376 381 382 384 [91] 389 399 400 402 408 413 416 417 418 419 426 429 437 441 443 [106] 453 456 467 474 477 490 492 496 504 507 508 509 517 524 527 [121] 528 531 532 534 536 538 539 541 542 543 544 545 546 547 552 [136] 553 558 560 570 571 581 583 587 593 594 596 597 605 612 613 [151] 618 620 625 629 638 642 647 649 653 655 656 672 675 681 686 [166] 699 701 702 712 714 716 721 725 726 735 744 753 754 756 759 [181] 765 766 769 779 781 782 785 787 797 804 813 825 827 837 840 [196] 844 852 853 857 860 865 866 869 870 872 873 883 884 887 888 [211] 890 891 893 908 909 912 915 916 921 927 930 952 962 963 969 [226] 974 980 982 986 987 988 992 997 1000 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: bisquare Robust Estimate of Location: lat long depth mag -21.54 182.35 369.29 4.54 Robust Estimate of Covariance: lat long depth mag lat 2.18e+01 4.82e+00 2.53e+02 -3.54e-01 long 4.82e+00 5.87e+00 -4.63e+02 7.45e-02 depth 2.53e+02 -4.63e+02 6.51e+04 -2.10e+01 mag -3.54e-01 7.45e-02 -2.10e+01 1.83e-01 -------------------------------------------------------- =================================================== > dodata(method="rocke") Call: dodata(method = "rocke") Data Set n p LOG(det) Time =================================================== heart 12 2 7.285196 Outliers: 3 [1] 2 6 12 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: height weight 34.3 26.1 Robust Estimate of Covariance: height weight height 105 159 weight 159 256 -------------------------------------------------------- starsCYG 47 2 -5.929361 Outliers: 7 [1] 7 9 11 14 20 30 34 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: log.Te log.light 4.42 4.93 Robust Estimate of Covariance: log.Te log.light log.Te 0.0193 0.0709 log.light 0.0709 0.3987 -------------------------------------------------------- phosphor 18 2 8.907518 Outliers: 3 [1] 1 6 10 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: inorg organic 15.8 39.4 Robust Estimate of Covariance: inorg organic inorg 196 252 organic 252 360 -------------------------------------------------------- stackloss 21 3 8.143313 Outliers: 4 [1] 1 2 3 21 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: Air.Flow Water.Temp Acid.Conc. 56.8 20.2 86.4 Robust Estimate of Covariance: Air.Flow Water.Temp Acid.Conc. Air.Flow 29.26 9.62 14.78 Water.Temp 9.62 8.54 6.25 Acid.Conc. 14.78 6.25 29.70 -------------------------------------------------------- coleman 20 5 4.001659 Outliers: 5 [1] 2 6 9 10 13 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: salaryP fatherWc sstatus teacherSc motherLev 2.81 40.27 2.11 25.01 6.27 Robust Estimate of Covariance: salaryP fatherWc sstatus teacherSc motherLev salaryP 0.2850 1.1473 2.0254 0.3536 0.0737 fatherWc 1.1473 798.0714 278.0145 6.4590 18.6357 sstatus 2.0254 278.0145 128.7601 4.0666 6.3845 teacherSc 0.3536 6.4590 4.0666 0.8749 0.2980 motherLev 0.0737 18.6357 6.3845 0.2980 0.4948 -------------------------------------------------------- salinity 28 3 3.455146 Outliers: 9 [1] 3 5 10 11 15 16 17 23 24 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: X1 X2 X3 9.89 3.10 22.46 Robust Estimate of Covariance: X1 X2 X3 X1 12.710 1.868 -4.135 X2 1.868 4.710 -0.663 X3 -4.135 -0.663 1.907 -------------------------------------------------------- wood 20 5 -35.020244 Outliers: 7 [1] 4 6 7 8 11 16 19 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: x1 x2 x3 x4 x5 0.588 0.123 0.534 0.535 0.891 Robust Estimate of Covariance: x1 x2 x3 x4 x5 x1 6.60e-03 1.25e-03 2.16e-03 -3.73e-04 -1.10e-03 x2 1.25e-03 3.30e-04 8.91e-04 -1.23e-05 2.62e-05 x3 2.16e-03 8.91e-04 4.55e-03 -4.90e-04 1.93e-04 x4 -3.73e-04 -1.23e-05 -4.90e-04 2.01e-03 1.36e-03 x5 -1.10e-03 2.62e-05 1.93e-04 1.36e-03 1.95e-03 -------------------------------------------------------- hbk 75 3 1.413303 Outliers: 14 [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: X1 X2 X3 1.56 1.77 1.68 Robust Estimate of Covariance: X1 X2 X3 X1 1.6483 0.0825 0.2133 X2 0.0825 1.6928 0.2334 X3 0.2133 0.2334 1.5334 -------------------------------------------------------- Animals 28 2 17.787210 Outliers: 11 [1] 2 6 7 9 12 14 15 16 24 25 28 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: body brain 60.6 150.2 Robust Estimate of Covariance: body brain body 10670 19646 brain 19646 41147 -------------------------------------------------------- milk 86 8 -25.169970 Outliers: 22 [1] 1 2 3 11 12 13 14 15 16 17 18 20 27 28 41 44 47 70 73 74 75 77 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: X1 X2 X3 X4 X5 X6 X7 X8 1.03 35.87 33.14 26.19 25.17 25.11 123.16 14.41 Robust Estimate of Covariance: X1 X2 X3 X4 X5 X6 X7 X1 4.47e-07 1.77e-04 1.94e-04 1.79e-04 1.60e-04 1.45e-04 6.45e-04 X2 1.77e-04 2.36e+00 4.03e-01 3.08e-01 2.08e-01 3.45e-01 2.18e+00 X3 1.94e-04 4.03e-01 1.13e+00 8.31e-01 8.08e-01 7.79e-01 9.83e-01 X4 1.79e-04 3.08e-01 8.31e-01 6.62e-01 6.22e-01 5.95e-01 7.82e-01 X5 1.60e-04 2.08e-01 8.08e-01 6.22e-01 6.51e-01 5.93e-01 7.60e-01 X6 1.45e-04 3.45e-01 7.79e-01 5.95e-01 5.93e-01 5.88e-01 7.81e-01 X7 6.45e-04 2.18e+00 9.83e-01 7.82e-01 7.60e-01 7.81e-01 4.81e+00 X8 2.47e-05 2.57e-01 2.00e-01 1.37e-01 1.13e-01 1.28e-01 4.38e-01 X8 X1 2.47e-05 X2 2.57e-01 X3 2.00e-01 X4 1.37e-01 X5 1.13e-01 X6 1.28e-01 X7 4.38e-01 X8 1.61e-01 -------------------------------------------------------- bushfire 38 5 21.641566 Outliers: 13 [1] 7 8 9 10 11 31 32 33 34 35 36 37 38 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: V1 V2 V3 V4 V5 111 150 256 214 276 Robust Estimate of Covariance: V1 V2 V3 V4 V5 V1 554 408 -2321 -464 -393 V2 408 343 -1361 -244 -215 V3 -2321 -1361 14690 3277 2684 V4 -464 -244 3277 783 629 V5 -393 -215 2684 629 509 -------------------------------------------------------- rice 105 5 -7.208835 Outliers: 8 [1] 9 14 40 42 49 57 58 71 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: Favor Appearance Taste Stickiness Toughness -0.21721 0.20948 -0.04581 0.15355 -0.00254 Robust Estimate of Covariance: Favor Appearance Taste Stickiness Toughness Favor 0.432 0.337 0.417 0.382 -0.201 Appearance 0.337 0.591 0.553 0.510 -0.295 Taste 0.417 0.553 0.735 0.683 -0.385 Stickiness 0.382 0.510 0.683 0.834 -0.462 Toughness -0.201 -0.295 -0.385 -0.462 0.408 -------------------------------------------------------- hemophilia 75 2 -7.453807 Outliers: 2 [1] 46 53 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: AHFactivity AHFantigen -0.2276 -0.0637 Robust Estimate of Covariance: AHFactivity AHFantigen AHFactivity 0.0405 0.0221 AHFantigen 0.0221 0.0263 -------------------------------------------------------- fish 159 6 13.110263 Outliers: 47 [1] 38 61 62 63 64 65 66 67 68 69 70 71 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 99 100 101 102 103 104 140 142 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: Weight Length1 Length2 Length3 Height Width 452.1 27.2 29.5 32.6 30.8 15.0 Robust Estimate of Covariance: Weight Length1 Length2 Length3 Height Width Weight 132559.85 2817.97 3035.69 3369.07 1231.68 112.19 Length1 2817.97 64.16 68.74 75.36 22.52 2.37 Length2 3035.69 68.74 73.77 81.12 25.57 2.47 Length3 3369.07 75.36 81.12 91.65 37.39 1.40 Height 1231.68 22.52 25.57 37.39 50.91 -3.92 Width 112.19 2.37 2.47 1.40 -3.92 1.87 -------------------------------------------------------- airquality 153 4 21.181656 Outliers: 13 [1] 6 7 11 14 17 20 23 30 34 53 63 77 107 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: Ozone Solar.R Wind Temp 40.21 198.33 9.76 79.35 Robust Estimate of Covariance: Ozone Solar.R Wind Temp Ozone 885.7 581.1 -57.3 226.4 Solar.R 581.1 8870.9 26.2 -15.1 Wind -57.3 26.2 11.8 -13.4 Temp 226.4 -15.1 -13.4 89.4 -------------------------------------------------------- attitude 30 7 27.836398 Outliers: 8 [1] 1 9 13 14 17 18 24 26 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: rating complaints privileges learning raises critical 64.0 65.4 50.5 54.9 63.1 72.6 advance 40.5 Robust Estimate of Covariance: rating complaints privileges learning raises critical advance rating 180.10 153.16 42.04 128.90 90.25 18.75 39.81 complaints 153.16 192.38 58.32 142.48 94.29 8.13 45.33 privileges 42.04 58.32 113.65 82.31 69.53 23.13 61.96 learning 128.90 142.48 82.31 156.99 101.74 13.22 49.64 raises 90.25 94.29 69.53 101.74 110.85 47.84 55.76 critical 18.75 8.13 23.13 13.22 47.84 123.00 36.97 advance 39.81 45.33 61.96 49.64 55.76 36.97 53.59 -------------------------------------------------------- attenu 182 5 9.726797 Outliers: 44 [1] 1 2 4 5 6 7 8 9 10 11 13 15 16 19 20 21 22 23 24 [20] 25 27 28 29 30 31 32 40 45 60 61 64 65 78 80 81 93 94 95 [39] 96 97 98 99 100 108 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: event mag station dist accel 16.39 5.82 60.89 27.97 0.12 Robust Estimate of Covariance: event mag station dist accel event 4.20e+01 -1.97e+00 1.44e+02 -3.50e+01 4.05e-02 mag -1.97e+00 5.05e-01 -4.78e+00 4.63e+00 4.19e-03 station 1.44e+02 -4.78e+00 1.47e+03 -5.74e+01 7.88e-01 dist -3.50e+01 4.63e+00 -5.74e+01 3.99e+02 -1.18e+00 accel 4.05e-02 4.19e-03 7.88e-01 -1.18e+00 7.71e-03 -------------------------------------------------------- USJudgeRatings 43 12 -46.356873 Outliers: 15 [1] 1 5 7 8 12 13 14 17 20 21 23 30 31 35 42 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: CONT INTG DMNR DILG CFMG DECI PREP FAMI ORAL WRIT PHYS RTEN 7.56 8.12 7.70 7.91 7.74 7.82 7.66 7.66 7.50 7.58 8.22 7.86 Robust Estimate of Covariance: CONT INTG DMNR DILG CFMG DECI PREP CONT 0.63426 -0.20121 -0.31858 -0.09578 0.00521 -0.00436 -0.07140 INTG -0.20121 0.28326 0.37540 0.27103 0.20362 0.19838 0.25706 DMNR -0.31858 0.37540 0.58265 0.33615 0.25649 0.24804 0.31696 DILG -0.09578 0.27103 0.33615 0.32588 0.27022 0.26302 0.32236 CFMG 0.00521 0.20362 0.25649 0.27022 0.25929 0.24217 0.27784 DECI -0.00436 0.19838 0.24804 0.26302 0.24217 0.23830 0.27284 PREP -0.07140 0.25706 0.31696 0.32236 0.27784 0.27284 0.35071 FAMI -0.07118 0.25858 0.29511 0.32582 0.27863 0.27657 0.35941 ORAL -0.11149 0.27055 0.33919 0.31768 0.27339 0.26739 0.34200 WRIT -0.10050 0.26857 0.32570 0.32327 0.27860 0.27201 0.34399 PHYS -0.09693 0.15339 0.18416 0.17089 0.13837 0.14895 0.18472 RTEN -0.15643 0.31793 0.40884 0.33863 0.27073 0.26854 0.34049 FAMI ORAL WRIT PHYS RTEN CONT -0.07118 -0.11149 -0.10050 -0.09693 -0.15643 INTG 0.25858 0.27055 0.26857 0.15339 0.31793 DMNR 0.29511 0.33919 0.32570 0.18416 0.40884 DILG 0.32582 0.31768 0.32327 0.17089 0.33863 CFMG 0.27863 0.27339 0.27860 0.13837 0.27073 DECI 0.27657 0.26739 0.27201 0.14895 0.26854 PREP 0.35941 0.34200 0.34399 0.18472 0.34049 FAMI 0.38378 0.35617 0.36094 0.19998 0.35048 ORAL 0.35617 0.34918 0.34808 0.19759 0.35217 WRIT 0.36094 0.34808 0.35242 0.19666 0.35090 PHYS 0.19998 0.19759 0.19666 0.14770 0.20304 RTEN 0.35048 0.35217 0.35090 0.20304 0.39451 -------------------------------------------------------- USArrests 50 4 19.206310 Outliers: 4 [1] 2 28 33 39 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: Murder Assault UrbanPop Rape 7.55 160.94 65.10 19.97 Robust Estimate of Covariance: Murder Assault UrbanPop Rape Murder 25.6 409.5 23.4 32.1 Assault 409.5 8530.9 676.9 669.4 UrbanPop 23.4 676.9 269.9 76.6 Rape 32.1 669.4 76.6 76.6 -------------------------------------------------------- longley 16 7 13.387132 Outliers: 4 [1] 1 2 3 4 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: GNP.deflator GNP Unemployed Armed.Forces Population 105.5 422.4 318.3 299.7 119.5 Year Employed 1956.1 66.5 Robust Estimate of Covariance: GNP.deflator GNP Unemployed Armed.Forces Population GNP.deflator 59.97 582.66 694.99 -237.75 46.12 GNP 582.66 5849.82 6383.68 -2207.26 461.15 Unemployed 694.99 6383.68 11155.03 -3104.18 534.25 Armed.Forces -237.75 -2207.26 -3104.18 1429.11 -171.28 Population 46.12 461.15 534.25 -171.28 36.79 Year 29.01 287.48 340.95 -112.61 22.85 Employed 18.99 193.66 186.31 -76.88 14.94 Year Employed GNP.deflator 29.01 18.99 GNP 287.48 193.66 Unemployed 340.95 186.31 Armed.Forces -112.61 -76.88 Population 22.85 14.94 Year 14.36 9.45 Employed 9.45 6.90 -------------------------------------------------------- Loblolly 84 3 7.757906 Outliers: 27 [1] 5 6 11 12 18 23 24 29 30 35 36 41 42 47 48 53 54 59 60 65 66 71 72 77 78 [26] 83 84 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: height age Seed 21.72 8.60 7.58 Robust Estimate of Covariance: height age Seed height 316.590 102.273 5.939 age 102.273 33.465 -0.121 Seed 5.939 -0.121 27.203 -------------------------------------------------------- quakes 1000 4 11.473431 Outliers: 237 [1] 7 12 15 17 22 25 27 28 32 37 40 41 45 48 53 [16] 63 64 73 78 87 91 92 94 99 108 110 117 118 119 120 [31] 121 122 126 133 136 141 143 145 148 152 154 155 157 159 160 [46] 163 166 170 174 176 192 205 222 226 230 239 243 244 250 251 [61] 252 254 258 263 267 268 271 283 292 297 300 301 305 311 312 [76] 318 320 321 325 328 330 331 334 352 357 360 365 368 376 381 [91] 382 384 389 399 400 402 408 410 413 416 417 418 419 426 429 [106] 437 441 443 453 456 467 474 477 490 492 496 504 507 508 509 [121] 517 524 527 528 531 532 534 536 538 539 541 542 543 544 545 [136] 546 547 552 553 558 560 570 571 581 583 587 593 594 596 597 [151] 605 612 613 618 620 625 629 638 642 647 649 653 655 656 672 [166] 675 681 686 699 701 702 712 714 716 721 725 726 735 744 753 [181] 754 756 759 765 766 769 779 781 782 785 787 797 804 813 825 [196] 827 837 840 844 852 853 857 860 865 866 869 870 872 873 883 [211] 884 887 888 890 891 893 908 909 912 915 916 921 927 930 952 [226] 962 963 969 974 980 982 986 987 988 992 997 1000 ------------- Call: CovSest(x = x, method = method) -> Method: S-estimates: Rocke type Robust Estimate of Location: lat long depth mag -21.45 182.54 351.18 4.55 Robust Estimate of Covariance: lat long depth mag lat 2.10e+01 4.66e+00 2.45e+02 -3.38e-01 long 4.66e+00 5.88e+00 -4.63e+02 9.36e-02 depth 2.45e+02 -4.63e+02 6.38e+04 -2.02e+01 mag -3.38e-01 9.36e-02 -2.02e+01 1.78e-01 -------------------------------------------------------- =================================================== > dodata(method="MM") Call: dodata(method = "MM") Data Set n p LOG(det) Time =================================================== heart 12 2 2.017701 Outliers: 1 [1] 6 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: height weight 40.0 37.7 Robust Estimate of Covariance: height weight height 99.2 205.7 weight 205.7 458.9 -------------------------------------------------------- starsCYG 47 2 -1.450032 Outliers: 7 [1] 7 9 11 14 20 30 34 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: log.Te log.light 4.41 4.94 Robust Estimate of Covariance: log.Te log.light log.Te 0.0180 0.0526 log.light 0.0526 0.3217 -------------------------------------------------------- phosphor 18 2 2.320721 Outliers: 1 [1] 6 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: inorg organic 12.3 41.4 Robust Estimate of Covariance: inorg organic inorg 94.2 67.2 organic 67.2 162.1 -------------------------------------------------------- stackloss 21 3 1.470031 Outliers: 0 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: Air.Flow Water.Temp Acid.Conc. 60.2 21.0 86.4 Robust Estimate of Covariance: Air.Flow Water.Temp Acid.Conc. Air.Flow 81.13 21.99 23.15 Water.Temp 21.99 10.01 6.43 Acid.Conc. 23.15 6.43 27.22 -------------------------------------------------------- coleman 20 5 0.491419 Outliers: 1 [1] 10 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: salaryP fatherWc sstatus teacherSc motherLev 2.74 43.14 3.65 25.07 6.32 Robust Estimate of Covariance: salaryP fatherWc sstatus teacherSc motherLev salaryP 0.1878 2.0635 1.0433 0.2721 0.0582 fatherWc 2.0635 670.2232 211.0609 4.3625 15.6083 sstatus 1.0433 211.0609 92.8743 2.6532 5.1816 teacherSc 0.2721 4.3625 2.6532 1.2757 0.1613 motherLev 0.0582 15.6083 5.1816 0.1613 0.4192 -------------------------------------------------------- salinity 28 3 0.734619 Outliers: 2 [1] 5 16 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: X1 X2 X3 10.46 2.66 23.15 Robust Estimate of Covariance: X1 X2 X3 X1 10.079 -0.024 -1.899 X2 -0.024 3.466 -1.817 X3 -1.899 -1.817 3.665 -------------------------------------------------------- wood 20 5 -3.202636 Outliers: 0 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: x1 x2 x3 x4 x5 0.550 0.133 0.506 0.511 0.909 Robust Estimate of Covariance: x1 x2 x3 x4 x5 x1 0.008454 -0.000377 0.003720 0.002874 -0.003065 x2 -0.000377 0.000516 -0.000399 -0.000933 0.000645 x3 0.003720 -0.000399 0.004186 0.001720 -0.001714 x4 0.002874 -0.000933 0.001720 0.003993 -0.001028 x5 -0.003065 0.000645 -0.001714 -0.001028 0.002744 -------------------------------------------------------- hbk 75 3 0.283145 Outliers: 14 [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: X1 X2 X3 1.54 1.79 1.68 Robust Estimate of Covariance: X1 X2 X3 X1 1.8016 0.0739 0.2000 X2 0.0739 1.8301 0.2295 X3 0.2000 0.2295 1.7101 -------------------------------------------------------- Animals 28 2 4.685129 Outliers: 10 [1] 2 6 7 9 12 14 15 16 24 25 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: body brain 82 148 Robust Estimate of Covariance: body brain body 21050 24534 brain 24534 35135 -------------------------------------------------------- milk 86 8 -1.437863 Outliers: 12 [1] 1 2 3 12 13 17 41 44 47 70 74 75 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: X1 X2 X3 X4 X5 X6 X7 X8 1.03 35.73 32.87 25.96 24.94 24.85 122.55 14.33 Robust Estimate of Covariance: X1 X2 X3 X4 X5 X6 X7 X1 1.08e-06 5.36e-04 6.80e-04 5.96e-04 5.87e-04 5.91e-04 2.22e-03 X2 5.36e-04 2.42e+00 7.07e-01 5.51e-01 4.89e-01 5.70e-01 3.08e+00 X3 6.80e-04 7.07e-01 1.64e+00 1.28e+00 1.25e+00 1.26e+00 2.38e+00 X4 5.96e-04 5.51e-01 1.28e+00 1.05e+00 1.01e+00 1.02e+00 2.01e+00 X5 5.87e-04 4.89e-01 1.25e+00 1.01e+00 1.05e+00 1.02e+00 1.96e+00 X6 5.91e-04 5.70e-01 1.26e+00 1.02e+00 1.02e+00 1.05e+00 2.01e+00 X7 2.22e-03 3.08e+00 2.38e+00 2.01e+00 1.96e+00 2.01e+00 9.22e+00 X8 1.68e-04 4.13e-01 3.37e-01 2.53e-01 2.34e-01 2.43e-01 8.81e-01 X8 X1 1.68e-04 X2 4.13e-01 X3 3.37e-01 X4 2.53e-01 X5 2.34e-01 X6 2.43e-01 X7 8.81e-01 X8 2.11e-01 -------------------------------------------------------- bushfire 38 5 2.443148 Outliers: 12 [1] 8 9 10 11 31 32 33 34 35 36 37 38 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: V1 V2 V3 V4 V5 109 149 258 215 276 Robust Estimate of Covariance: V1 V2 V3 V4 V5 V1 708 538 -2705 -558 -464 V2 538 497 -1376 -248 -216 V3 -2705 -1376 20521 4833 3914 V4 -558 -248 4833 1217 969 V5 -464 -216 3914 969 778 -------------------------------------------------------- rice 105 5 -0.724874 Outliers: 5 [1] 9 42 49 58 71 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: Favor Appearance Taste Stickiness Toughness -0.2653 0.0969 -0.1371 0.0483 0.0731 Robust Estimate of Covariance: Favor Appearance Taste Stickiness Toughness Favor 0.421 0.349 0.427 0.405 -0.191 Appearance 0.349 0.605 0.565 0.553 -0.316 Taste 0.427 0.565 0.725 0.701 -0.378 Stickiness 0.405 0.553 0.701 0.868 -0.484 Toughness -0.191 -0.316 -0.378 -0.484 0.464 -------------------------------------------------------- hemophilia 75 2 -1.868949 Outliers: 2 [1] 11 36 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: AHFactivity AHFantigen -0.2342 -0.0333 Robust Estimate of Covariance: AHFactivity AHFantigen AHFactivity 0.0309 0.0122 AHFantigen 0.0122 0.0231 -------------------------------------------------------- fish 159 6 1.285876 Outliers: 20 [1] 61 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 [20] 142 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: Weight Length1 Length2 Length3 Height Width 352.7 24.3 26.4 29.2 29.7 14.6 Robust Estimate of Covariance: Weight Length1 Length2 Length3 Height Width Weight 1.20e+05 2.89e+03 3.12e+03 3.51e+03 1.49e+03 2.83e+02 Length1 2.89e+03 7.73e+01 8.35e+01 9.28e+01 3.73e+01 9.26e+00 Length2 3.12e+03 8.35e+01 9.04e+01 1.01e+02 4.16e+01 1.01e+01 Length3 3.51e+03 9.28e+01 1.01e+02 1.14e+02 5.37e+01 1.01e+01 Height 1.49e+03 3.73e+01 4.16e+01 5.37e+01 6.75e+01 3.22e+00 Width 2.83e+02 9.26e+00 1.01e+01 1.01e+01 3.22e+00 4.18e+00 -------------------------------------------------------- airquality 153 4 2.684374 Outliers: 6 [1] 7 14 23 30 34 77 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: Ozone Solar.R Wind Temp 40.35 186.21 9.86 78.09 Robust Estimate of Covariance: Ozone Solar.R Wind Temp Ozone 951.0 959.9 -62.5 224.6 Solar.R 959.9 8629.9 -28.1 244.9 Wind -62.5 -28.1 11.6 -15.8 Temp 224.6 244.9 -15.8 93.1 -------------------------------------------------------- attitude 30 7 2.091968 Outliers: 4 [1] 14 16 18 24 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: rating complaints privileges learning raises critical 65.0 66.5 52.4 56.2 65.3 75.6 advance 42.7 Robust Estimate of Covariance: rating complaints privileges learning raises critical advance rating 143.5 123.4 62.4 92.5 79.2 17.7 28.2 complaints 123.4 159.8 83.9 99.7 96.0 27.3 44.0 privileges 62.4 83.9 133.5 78.6 62.0 13.4 46.4 learning 92.5 99.7 78.6 136.0 90.9 18.9 62.6 raises 79.2 96.0 62.0 90.9 107.6 34.6 63.3 critical 17.7 27.3 13.4 18.9 34.6 84.9 25.9 advance 28.2 44.0 46.4 62.6 63.3 25.9 94.4 -------------------------------------------------------- attenu 182 5 1.148032 Outliers: 21 [1] 2 7 8 9 10 11 15 16 24 25 28 29 30 31 32 64 65 94 95 [20] 96 100 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: event mag station dist accel 15.36 5.95 58.11 33.56 0.14 Robust Estimate of Covariance: event mag station dist accel event 4.88e+01 -2.74e+00 1.53e+02 -1.14e+02 5.95e-02 mag -2.74e+00 5.32e-01 -6.29e+00 1.10e+01 9.37e-03 station 1.53e+02 -6.29e+00 1.29e+03 -2.95e+02 1.04e+00 dist -1.14e+02 1.10e+01 -2.95e+02 1.13e+03 -2.41e+00 accel 5.95e-02 9.37e-03 1.04e+00 -2.41e+00 1.70e-02 -------------------------------------------------------- USJudgeRatings 43 12 -1.683847 Outliers: 7 [1] 5 7 12 13 14 23 31 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: CONT INTG DMNR DILG CFMG DECI PREP FAMI ORAL WRIT PHYS RTEN 7.45 8.15 7.74 7.87 7.67 7.74 7.65 7.65 7.50 7.57 8.17 7.85 Robust Estimate of Covariance: CONT INTG DMNR DILG CFMG DECI PREP FAMI CONT 0.9403 -0.2500 -0.3953 -0.1418 -0.0176 -0.0620 -0.1304 -0.1517 INTG -0.2500 0.6314 0.8479 0.6889 0.5697 0.5386 0.7007 0.6985 DMNR -0.3953 0.8479 1.2186 0.9027 0.7613 0.7232 0.9191 0.9055 DILG -0.1418 0.6889 0.9027 0.8474 0.7344 0.6949 0.8751 0.8655 CFMG -0.0176 0.5697 0.7613 0.7344 0.6904 0.6442 0.7683 0.7594 DECI -0.0620 0.5386 0.7232 0.6949 0.6442 0.6219 0.7362 0.7360 PREP -0.1304 0.7007 0.9191 0.8751 0.7683 0.7362 0.9370 0.9357 FAMI -0.1517 0.6985 0.9055 0.8655 0.7594 0.7360 0.9357 0.9547 ORAL -0.1866 0.7375 0.9841 0.8816 0.7747 0.7433 0.9400 0.9496 WRIT -0.1881 0.7208 0.9516 0.8711 0.7646 0.7357 0.9302 0.9439 PHYS -0.1407 0.4673 0.6261 0.5661 0.5105 0.5039 0.5996 0.6112 RTEN -0.2494 0.7921 1.0688 0.9167 0.7902 0.7585 0.9533 0.9561 ORAL WRIT PHYS RTEN CONT -0.1866 -0.1881 -0.1407 -0.2494 INTG 0.7375 0.7208 0.4673 0.7921 DMNR 0.9841 0.9516 0.6261 1.0688 DILG 0.8816 0.8711 0.5661 0.9167 CFMG 0.7747 0.7646 0.5105 0.7902 DECI 0.7433 0.7357 0.5039 0.7585 PREP 0.9400 0.9302 0.5996 0.9533 FAMI 0.9496 0.9439 0.6112 0.9561 ORAL 0.9712 0.9558 0.6271 0.9933 WRIT 0.9558 0.9483 0.6135 0.9725 PHYS 0.6271 0.6135 0.4816 0.6549 RTEN 0.9933 0.9725 0.6549 1.0540 -------------------------------------------------------- USArrests 50 4 2.411726 Outliers: 3 [1] 2 33 39 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: Murder Assault UrbanPop Rape 7.52 163.86 65.66 20.64 Robust Estimate of Covariance: Murder Assault UrbanPop Rape Murder 19.05 295.96 8.32 23.40 Assault 295.96 6905.03 396.53 523.49 UrbanPop 8.32 396.53 202.98 62.81 Rape 23.40 523.49 62.81 79.10 -------------------------------------------------------- longley 16 7 1.038316 Outliers: 5 [1] 1 2 3 4 5 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: GNP.deflator GNP Unemployed Armed.Forces Population 107.5 440.4 339.4 293.0 120.9 Year Employed 1957.0 67.2 Robust Estimate of Covariance: GNP.deflator GNP Unemployed Armed.Forces Population GNP.deflator 100.4 953.8 1140.8 -501.8 74.3 GNP 953.8 9434.3 10084.3 -4573.8 731.3 Unemployed 1140.8 10084.3 19644.6 -6296.3 848.4 Armed.Forces -501.8 -4573.8 -6296.3 3192.3 -348.5 Population 74.3 731.3 848.4 -348.5 57.7 Year 46.3 450.7 537.0 -230.7 35.3 Employed 30.8 310.2 273.8 -159.4 23.3 Year Employed GNP.deflator 46.3 30.8 GNP 450.7 310.2 Unemployed 537.0 273.8 Armed.Forces -230.7 -159.4 Population 35.3 23.3 Year 21.9 14.6 Employed 14.6 11.2 -------------------------------------------------------- Loblolly 84 3 1.481317 Outliers: 0 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: height age Seed 31.93 12.79 7.48 Robust Estimate of Covariance: height age Seed height 440.644 165.652 6.958 age 165.652 63.500 0.681 Seed 6.958 0.681 16.564 -------------------------------------------------------- quakes 1000 4 1.576855 Outliers: 218 [1] 7 12 15 17 22 27 32 37 40 41 45 48 53 63 64 [16] 73 78 87 91 92 94 99 108 110 117 118 119 120 121 122 [31] 126 133 136 141 143 145 148 152 154 155 157 159 160 163 170 [46] 192 205 222 226 230 239 243 250 251 252 254 258 263 267 268 [61] 271 283 292 300 301 305 311 312 318 320 321 325 328 330 334 [76] 352 357 360 365 381 382 384 389 400 402 408 413 416 417 419 [91] 429 437 441 443 453 456 467 474 477 490 492 496 504 507 508 [106] 509 517 524 527 528 531 532 534 536 538 539 541 542 543 544 [121] 545 546 547 552 553 560 571 581 583 587 593 594 596 597 605 [136] 612 613 618 620 625 629 638 642 647 649 653 655 656 672 675 [151] 681 686 699 701 702 712 714 716 721 725 726 735 744 754 756 [166] 759 765 766 769 779 781 782 785 787 797 804 813 825 827 837 [181] 840 844 852 853 857 860 865 866 869 870 872 873 883 884 887 [196] 888 890 891 893 908 909 912 915 916 921 927 930 962 963 969 [211] 974 980 982 986 987 988 997 1000 ------------- Call: CovMMest(x = x) -> Method: MM-estimates Robust Estimate of Location: lat long depth mag -21.74 182.37 356.37 4.56 Robust Estimate of Covariance: lat long depth mag lat 2.97e+01 6.53e+00 3.46e+02 -4.66e-01 long 6.53e+00 6.92e+00 -5.05e+02 5.62e-02 depth 3.46e+02 -5.05e+02 7.39e+04 -2.51e+01 mag -4.66e-01 5.62e-02 -2.51e+01 2.32e-01 -------------------------------------------------------- =================================================== > ##dogen() > ##cat('Time elapsed: ', proc.time(),'\n') # for ``statistical reasons'' > > proc.time() user system elapsed 6.96 0.90 7.87