File: tmcd.Rout.save

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R version 2.9.0 Under development (unstable) (2009-01-20 r47658)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(robustbase)
> 
> source(system.file("test_MCD.R", package = "robustbase"))
> ##          ../inst/test_MCD.R
> 
> ## -- now do it:
> options(digits = 5)
> set.seed(101) # <<-- sub-sampling algorithm now based on R's RNG and seed
> doMCDdata()

Call:  doMCDdata() 
Data Set               n   p  Half   LOG(obj)  Time [ms]
========================================================
               heart  12   2   7     5.678742 
Best subsample: 
[1]  1  3  4  5  7  9 11
Outliers:  0 
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  5.68 
Robust Estimate of Location:
height  weight  
  38.3    33.1  
Robust Estimate of Covariance:
        height  weight
height     157     303
weight     303     660
--------------------------------------------------------
            phosphor  18   2  10     6.878847 
Best subsample: 
 [1]  3  5  8  9 11 12 13 14 15 17
Outliers:  2 
[1] 1 6
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  6.88 
Robust Estimate of Location:
  inorg  organic  
   13.4     38.8  
Robust Estimate of Covariance:
         inorg  organic
inorg      181      184
organic    184      256
--------------------------------------------------------
            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:  6 
[1]  7 11 14 20 30 34
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  -8.03 
Robust Estimate of Location:
   log.Te  log.light  
     4.41       4.95  
Robust Estimate of Covariance:
           log.Te  log.light
log.Te     0.0171     0.0511
log.light  0.0511     0.3555
--------------------------------------------------------
           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
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  5.47 
Robust Estimate of Location:
  Air.Flow  Water.Temp  Acid.Conc.  
      59.5        20.8        87.3  
Robust Estimate of Covariance:
            Air.Flow  Water.Temp  Acid.Conc.
Air.Flow        12.6        11.7        11.5
Water.Temp      11.7        18.5        12.3
Acid.Conc.      11.5        12.3        46.6
--------------------------------------------------------
             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
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  1.29 
Robust Estimate of Location:
  salaryP   fatherWc    sstatus  teacherSc  motherLev  
     2.76      48.38       6.12      25.00       6.40  
Robust Estimate of Covariance:
           salaryP  fatherWc  sstatus  teacherSc  motherLev
salaryP      0.381      2.69   -0.400      0.228      0.113
fatherWc     2.685   1959.47  496.858     18.948     51.871
sstatus     -0.400    496.86  180.236      5.762     15.230
teacherSc    0.228     18.95    5.762      1.180      0.835
motherLev    0.113     51.87   15.230      0.835      1.567
--------------------------------------------------------
            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
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  1.33 
Robust Estimate of Location:
   X1     X2     X3  
10.08   2.78  22.78  
Robust Estimate of Covariance:
       X1     X2     X3
X1  13.87   1.34  -4.24
X2   1.34   5.10  -1.92
X3  -4.24  -1.92   3.17
--------------------------------------------------------
                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
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  -36.3 
Robust Estimate of Location:
   x1     x2     x3     x4     x5  
0.587  0.122  0.531  0.538  0.892  
Robust Estimate of Covariance:
          x1         x2        x3         x4         x5
x1   0.01507   2.83e-03   0.00474  -8.81e-04  -2.45e-03
x2   0.00283   7.29e-04   0.00191  -7.82e-05   3.55e-05
x3   0.00474   1.91e-03   0.00997  -1.31e-03   5.30e-04
x4  -0.00088  -7.82e-05  -0.00131   4.28e-03   2.75e-03
x5  -0.00245   3.55e-05   0.00053   2.75e-03   4.16e-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
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  -1.05 
Robust Estimate of Location:
  X1    X2    X3  
1.54  1.78  1.69  
Robust Estimate of Covariance:
        X1      X2     X3
X1  1.6528  0.0741  0.171
X2  0.0741  1.6823  0.205
X3  0.1713  0.2055  1.562
--------------------------------------------------------
             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:  13 
 [1]  2  6  7  8  9 12 13 14 15 16 24 25 28
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  14.6 
Robust Estimate of Location:
 body  brain  
 18.7   64.9  
Robust Estimate of Covariance:
       body  brain
body   2511   4258
brain  4258  15257
--------------------------------------------------------
                milk  86   8  47   -28.848323 
Best subsample: 
 [1]  5  7  8  9 10 21 22 24 26 30 31 32 33 34 35 36 39 45 46 51 53 54 55 56 57
[26] 58 59 60 61 62 63 64 65 66 67 68 69 71 72 76 78 79 81 82 83 84 86
Outliers:  20 
 [1]  1  2  3 11 12 13 14 15 16 17 18 20 27 41 44 47 70 74 75 77
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  -28.8 
Robust Estimate of Location:
    X1      X2      X3      X4      X5      X6      X7      X8  
  1.03   35.89   33.08   26.14   25.12   25.05  123.17   14.38  
Robust Estimate of Covariance:
          X1        X2        X3        X4        X5        X6      X7
X1  5.16e-07  0.000141  0.000179  0.000175  0.000156  0.000135  0.0007
X2  1.41e-04  2.274487  0.283407  0.224349  0.123111  0.286851  2.0115
X3  1.79e-04  0.283407  1.338103  0.991617  0.977699  0.968312  0.8373
X4  1.75e-04  0.224349  0.991617  0.795728  0.760376  0.746050  0.6976
X5  1.56e-04  0.123111  0.977699  0.760376  0.806266  0.761894  0.6790
X6  1.35e-04  0.286851  0.968312  0.746050  0.761894  0.773555  0.7223
X7  7.00e-04  2.011544  0.837316  0.697578  0.678976  0.722292  4.7856
X8  1.68e-05  0.261205  0.227169  0.155399  0.129194  0.147308  0.4377
          X8
X1  1.68e-05
X2  2.61e-01
X3  2.27e-01
X4  1.55e-01
X5  1.29e-01
X6  1.47e-01
X7  4.38e-01
X8  1.86e-01
--------------------------------------------------------
            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
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  18.1 
Robust Estimate of Location:
 V1   V2   V3   V4   V5  
105  147  274  218  279  
Robust Estimate of Covariance:
       V1     V2     V3    V4    V5
V1    567    439  -2771  -624  -509
V2    439    387  -1843  -376  -318
V3  -2771  -1843  16367  4021  3196
V4   -624   -376   4021  1059   827
V5   -509   -318   3196   827   652
--------------------------------------------------------
========================================================
> ##                vvvv no timing for 'R CMD Rdiff' outputs
> doMCDdata(nrep = 12, time=FALSE)

Call:  doMCDdata(nrep = 12, time = FALSE) 
Data Set               n   p  Half   LOG(obj)  Time [ms]
========================================================
               heart  12   2   7     5.678742 
Best subsample: 
[1]  1  3  4  5  7  9 11
Outliers:  0 
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  5.68 
Robust Estimate of Location:
height  weight  
  38.3    33.1  
Robust Estimate of Covariance:
        height  weight
height     157     303
weight     303     660
--------------------------------------------------------
            phosphor  18   2  10     6.878847 
Best subsample: 
 [1]  3  5  8  9 11 12 13 14 15 17
Outliers:  2 
[1] 1 6
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  6.88 
Robust Estimate of Location:
  inorg  organic  
   13.4     38.8  
Robust Estimate of Covariance:
         inorg  organic
inorg      181      184
organic    184      256
--------------------------------------------------------
            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:  6 
[1]  7 11 14 20 30 34
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  -8.03 
Robust Estimate of Location:
   log.Te  log.light  
     4.41       4.95  
Robust Estimate of Covariance:
           log.Te  log.light
log.Te     0.0171     0.0511
log.light  0.0511     0.3555
--------------------------------------------------------
           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
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  5.47 
Robust Estimate of Location:
  Air.Flow  Water.Temp  Acid.Conc.  
      59.5        20.8        87.3  
Robust Estimate of Covariance:
            Air.Flow  Water.Temp  Acid.Conc.
Air.Flow        12.6        11.7        11.5
Water.Temp      11.7        18.5        12.3
Acid.Conc.      11.5        12.3        46.6
--------------------------------------------------------
             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
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  1.29 
Robust Estimate of Location:
  salaryP   fatherWc    sstatus  teacherSc  motherLev  
     2.76      48.38       6.12      25.00       6.40  
Robust Estimate of Covariance:
           salaryP  fatherWc  sstatus  teacherSc  motherLev
salaryP      0.381      2.69   -0.400      0.228      0.113
fatherWc     2.685   1959.47  496.858     18.948     51.871
sstatus     -0.400    496.86  180.236      5.762     15.230
teacherSc    0.228     18.95    5.762      1.180      0.835
motherLev    0.113     51.87   15.230      0.835      1.567
--------------------------------------------------------
            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
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  1.33 
Robust Estimate of Location:
   X1     X2     X3  
10.08   2.78  22.78  
Robust Estimate of Covariance:
       X1     X2     X3
X1  13.87   1.34  -4.24
X2   1.34   5.10  -1.92
X3  -4.24  -1.92   3.17
--------------------------------------------------------
                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
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  -36.3 
Robust Estimate of Location:
   x1     x2     x3     x4     x5  
0.587  0.122  0.531  0.538  0.892  
Robust Estimate of Covariance:
          x1         x2        x3         x4         x5
x1   0.01507   2.83e-03   0.00474  -8.81e-04  -2.45e-03
x2   0.00283   7.29e-04   0.00191  -7.82e-05   3.55e-05
x3   0.00474   1.91e-03   0.00997  -1.31e-03   5.30e-04
x4  -0.00088  -7.82e-05  -0.00131   4.28e-03   2.75e-03
x5  -0.00245   3.55e-05   0.00053   2.75e-03   4.16e-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
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  -1.05 
Robust Estimate of Location:
  X1    X2    X3  
1.54  1.78  1.69  
Robust Estimate of Covariance:
        X1      X2     X3
X1  1.6528  0.0741  0.171
X2  0.0741  1.6823  0.205
X3  0.1713  0.2055  1.562
--------------------------------------------------------
             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:  13 
 [1]  2  6  7  8  9 12 13 14 15 16 24 25 28
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  14.6 
Robust Estimate of Location:
 body  brain  
 18.7   64.9  
Robust Estimate of Covariance:
       body  brain
body   2511   4258
brain  4258  15257
--------------------------------------------------------
                milk  86   8  47   -28.902301 
Best subsample: 
 [1]  6  7  8  9 10 19 21 22 23 24 25 26 30 33 34 35 36 37 38 39 45 46 53 54 55
[26] 56 57 58 59 60 61 62 63 64 65 66 67 69 71 72 76 78 79 80 81 82 83
Outliers:  19 
 [1]  1  2  3 11 12 13 14 15 16 17 18 27 41 44 47 70 74 75 77
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  -28.9 
Robust Estimate of Location:
    X1      X2      X3      X4      X5      X6      X7      X8  
  1.03   35.97   33.13   26.17   25.15   25.08  123.18   14.39  
Robust Estimate of Covariance:
          X1        X2        X3        X4        X5        X6        X7
X1  6.21e-07  6.11e-05  0.000222  0.000220  0.000195  0.000181  0.000813
X2  6.11e-05  1.91e+00  0.305315  0.234515  0.151617  0.261667  2.081023
X3  2.22e-04  3.05e-01  1.524243  1.122585  1.092155  1.120191  0.884748
X4  2.20e-04  2.35e-01  1.122585  0.891433  0.844566  0.861078  0.727338
X5  1.95e-04  1.52e-01  1.092155  0.844566  0.878407  0.860894  0.709359
X6  1.81e-04  2.62e-01  1.120191  0.861078  0.860894  0.905852  0.729376
X7  8.13e-04  2.08e+00  0.884748  0.727338  0.709359  0.729376  5.130073
X8  8.02e-06  3.42e-01  0.261602  0.167884  0.146623  0.160590  0.506099
          X8
X1  8.02e-06
X2  3.42e-01
X3  2.62e-01
X4  1.68e-01
X5  1.47e-01
X6  1.61e-01
X7  5.06e-01
X8  2.04e-01
--------------------------------------------------------
            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
-------------
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = x)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  18.1 
Robust Estimate of Location:
 V1   V2   V3   V4   V5  
105  147  274  218  279  
Robust Estimate of Covariance:
       V1     V2     V3    V4    V5
V1    567    439  -2771  -624  -509
V2    439    387  -1843  -376  -318
V3  -2771  -1843  16367  4021  3196
V4   -624   -376   4021  1059   827
V5   -509   -318   3196   827   652
--------------------------------------------------------
========================================================
> doMCDdata(nrep = 12, time=FALSE, method = "MASS")

Call:  doMCDdata(nrep = 12, time = FALSE, method = "MASS") 
Data Set               n   p  Half   LOG(obj)  Time [ms]
========================================================
               heart  12   2   7     5.678742 
Best subsample: 
[1]  1  3  4  5  7  9 11
Outliers:  0 
-------------
$center
height weight 
40.358 38.125 

$cov
       height weight
height 142.46 298.91
weight 298.91 679.01

$msg
[1] "0 singular samples of size 3 out of 220"

$crit
[1] 5.6787

$best
[1]  1  3  4  5  7  9 11

$n.obs
[1] 12

--------------------------------------------------------
            phosphor  18   2  10     6.878847 
Best subsample: 
 [1]  3  5  8  9 11 12 13 14 15 17
Outliers:  0 
-------------
$center
  inorg organic 
 15.215  39.385 

$cov
         inorg organic
inorg    95.47  116.49
organic 116.49  171.76

$msg
[1] "1 singular samples of size 3 out of 816"

$crit
[1] 6.8788

$best
 [1]  3  5  8  9 11 12 13 14 15 17

$n.obs
[1] 18

--------------------------------------------------------
            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
[26] 47
Outliers:  0 
-------------
$center
   log.Te log.light 
   4.4127    4.9335 

$cov
            log.Te log.light
log.Te    0.011508  0.038513
log.light 0.038513  0.241013

$msg
[1] "9 singular samples of size 3 out of 1500"

$crit
[1] -8.0312

$best
 [1]  1  2  4  6  8 10 12 13 16 24 25 26 28 32 33 37 38 39 40 41 42 43 44 45 46
[26] 47

$n.obs
[1] 47

--------------------------------------------------------
           stackloss  21   3  12     5.472581 
Best subsample: 
 [1]  4  5  6  7  8  9 10 11 12 13 14 20
Outliers:  0 
-------------
$center
  Air.Flow Water.Temp Acid.Conc. 
    56.706     20.235     85.529 

$cov
           Air.Flow Water.Temp Acid.Conc.
Air.Flow    23.4706     7.5735    16.1029
Water.Temp   7.5735     6.3162     5.3676
Acid.Conc.  16.1029     5.3676    32.3897

$msg
[1] "90 singular samples of size 4 out of 2000"

$crit
[1] 5.4726

$best
 [1]  4  5  6  7  8  9 10 11 12 13 14 20

$n.obs
[1] 21

--------------------------------------------------------
             coleman  20   5  13     1.286808 
Best subsample: 
 [1]  2  3  4  5  7  8 12 13 14 16 17 19 20
Outliers:  0 
-------------
$center
  salaryP  fatherWc   sstatus teacherSc motherLev 
   2.8253   44.6267    4.7133   25.1240    6.3320 

$cov
           salaryP  fatherWc   sstatus teacherSc motherLev
salaryP    0.18916  -0.30888   0.14262   0.17971   0.02461
fatherWc  -0.30888 683.87325 196.89588   3.30523  17.29381
sstatus    0.14262 196.89588  85.94311   1.68507   5.58631
teacherSc  0.17971   3.30523   1.68507   0.51571   0.21891
motherLev  0.02461  17.29381   5.58631   0.21891   0.50172

$msg
[1] "0 singular samples of size 6 out of 3000"

$crit
[1] 1.2868

$best
 [1]  2  3  4  5  7  8 12 13 14 16 17 19 20

$n.obs
[1] 20

--------------------------------------------------------
            salinity  28   3  16     1.326364 
Best subsample: 
 [1]  1  2  6  7  8 12 13 14 18 20 21 22 25 26 27 28
Outliers:  0 
-------------
$center
     X1      X2      X3 
10.0826  2.7826 22.7777 

$cov
         X1       X2      X3
X1  9.14332  0.88241 -2.7916
X2  0.88241  3.35968 -1.2622
X3 -2.79160 -1.26222  2.0924

$msg
[1] "4 singular samples of size 4 out of 2000"

$crit
[1] 1.3264

$best
 [1]  1  2  6  7  8 12 13 14 18 20 21 22 25 26 27 28

$n.obs
[1] 28

--------------------------------------------------------
                wood  20   5  13   -36.270094 
Best subsample: 
 [1]  1  2  3  5  9 10 12 13 14 15 17 18 20
Outliers:  0 
-------------
$center
     x1      x2      x3      x4      x5 
0.57613 0.12294 0.53127 0.53760 0.88913 

$cov
            x1         x2          x3          x4          x5
x1  5.2757e-03 7.8749e-04  1.2965e-03 -2.0514e-05 -4.0002e-04
x2  7.8749e-04 2.2023e-04  5.4362e-04  2.3846e-05  2.7230e-05
x3  1.2965e-03 5.4362e-04  3.0435e-03 -7.0560e-04 -4.4395e-05
x4 -2.0514e-05 2.3846e-05 -7.0560e-04  2.1388e-03  1.3511e-03
x5 -4.0002e-04 2.7230e-05 -4.4395e-05  1.3511e-03  1.5946e-03

$msg
[1] "0 singular samples of size 6 out of 3000"

$crit
[1] -36.27

$best
 [1]  1  2  3  5  9 10 12 13 14 15 17 18 20

$n.obs
[1] 20

--------------------------------------------------------
                 hbk  75   3  39    -1.047858 
Best subsample: 
 [1] 15 16 17 18 19 20 21 22 23 24 26 27 31 32 33 35 36 37 38 40 43 49 50 51 54
[26] 55 56 58 59 61 63 64 66 67 70 71 72 73 74
Outliers:  0 
-------------
$center
    X1     X2     X3 
1.5583 1.8033 1.6600 

$cov
         X1       X2      X3
X1 1.124845 0.022175 0.15373
X2 0.022175 1.138972 0.18149
X3 0.153729 0.181492 1.04346

$msg
[1] "1 singular samples of size 4 out of 2000"

$crit
[1] -1.0479

$best
 [1] 15 16 17 18 19 20 21 22 23 24 26 27 31 32 33 35 36 37 38 40 43 49 50 51 54
[26] 55 56 58 59 61 63 64 66 67 70 71 72 73 74

$n.obs
[1] 75

--------------------------------------------------------
             Animals  28   2  15    14.555543 
Best subsample: 
 [1]  1  3  4  5 10 11 17 18 19 20 21 22 23 26 27
Outliers:  0 
-------------
$center
   body   brain 
 48.331 127.321 

$cov
        body   brain
body  4978.6  7801.4
brain 7801.4 21693.7

$msg
[1] "0 singular samples of size 3 out of 3276"

$crit
[1] 14.556

$best
 [1]  1  3  4  5 10 11 17 18 19 20 21 22 23 26 27

$n.obs
[1] 28

--------------------------------------------------------
                milk  86   8  47   -28.931843 
Best subsample: 
 [1]  5  7  8  9 10 22 23 24 26 30 31 32 33 34 35 37 38 39 45 46 49 51 53 54 55
[26] 56 57 58 59 60 61 63 64 65 66 67 68 69 71 72 76 78 79 81 83 84 86
Outliers:  0 
-------------
$center
      X1       X2       X3       X4       X5       X6       X7       X8 
  1.0302  35.7571  33.0540  26.1206  25.1000  25.0365 122.9397  14.3559 

$cov
           X1         X2         X3         X4         X5         X6         X7
X1 4.2168e-07 8.0438e-05 0.00016232 0.00015533 0.00013742 0.00012898 0.00056354
X2 8.0438e-05 1.4057e+00 0.19735023 0.14557604 0.09112903 0.17788018 1.15253456
X3 1.6232e-04 1.9735e-01 1.06155658 0.78306196 0.77129032 0.77961086 0.62201741
X4 1.5533e-04 1.4558e-01 0.78306196 0.62069636 0.59419355 0.59568612 0.50932924
X5 1.3742e-04 9.1129e-02 0.77129032 0.59419355 0.62419355 0.60209677 0.51435484
X6 1.2898e-04 1.7788e-01 0.77961086 0.59568612 0.60209677 0.62558116 0.51594726
X7 5.6354e-04 1.1525e+00 0.62201741 0.50932924 0.51435484 0.51594726 3.12630312
X8 3.1754e-06 1.0393e-01 0.15537148 0.10339299 0.08783871 0.09729826 0.19106964
           X8
X1 3.1754e-06
X2 1.0393e-01
X3 1.5537e-01
X4 1.0339e-01
X5 8.7839e-02
X6 9.7298e-02
X7 1.9107e-01
X8 1.0417e-01

$msg
[1] "40 singular samples of size 9 out of 3000"

$crit
[1] -28.932

$best
 [1]  5  7  8  9 10 22 23 24 26 30 31 32 33 34 35 37 38 39 45 46 49 51 53 54 55
[26] 56 57 58 59 60 61 63 64 65 66 67 68 69 71 72 76 78 79 81 83 84 86

$n.obs
[1] 86

--------------------------------------------------------
            bushfire  38   5  22    18.135810 
Best subsample: 
 [1]  1  2  3  4  5  6 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Outliers:  0 
-------------
$center
    V1     V2     V3     V4     V5 
109.38 148.23 250.96 212.38 274.50 

$cov
         V1       V2       V3       V4      V5
V1   361.69  270.748 -1549.42 -324.394 -270.24
V2   270.75  272.905  -624.23  -86.732  -74.12
V3 -1549.42 -624.231 12072.60 2940.415 2419.98
V4  -324.39  -86.732  2940.42  760.886  619.08
V5  -270.24  -74.120  2419.98  619.080  507.46

$msg
[1] "0 singular samples of size 6 out of 3000"

$crit
[1] 18.136

$best
 [1]  1  2  3  4  5  6 14 15 16 17 18 19 20 21 22 23 24 25 26 27

$n.obs
[1] 38

--------------------------------------------------------
========================================================
> 
> ###--- now the "close to singular" mahalanobis case:
> (c3 <- covMcd(mort3))
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = mort3)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  37.6 
Robust Estimate of Location:
  MO70    MAGE    CI68    MDOC    DENS    NONW    EDUC    IN69  
112.62  287.63  164.63  153.01   19.54    2.21  557.37  107.18  
Robust Estimate of Covariance:
         MO70      MAGE     CI68     MDOC     DENS     NONW  EDUC     IN69
MO70   645.32   567.286   125.06   109.26    -5.63   13.150  -904  -133.69
MAGE   567.29   860.391    -2.96   284.95   -95.30   -0.193  -500     5.57
CI68   125.06    -2.955   799.93  -357.48   -46.46    7.476  -839     7.38
MDOC   109.26   284.954  -357.48  2126.21   -89.66    1.462   423   121.61
DENS    -5.63   -95.297   -46.46   -89.66   181.24   10.686  -375   -62.28
NONW    13.15    -0.193     7.48     1.46    10.69    2.534   -98    -9.62
EDUC  -903.51  -500.437  -838.81   423.16  -374.60  -98.010  6789   511.09
IN69  -133.69     5.571     7.38   121.61   -62.28   -9.615   511   133.70
> ## rescale variables:
> scaleV <- c(0.1, 0.1, 1, 1, .001, 0.1, 0.1, 100)
> mm <- data.matrix(mort3) * rep(scaleV, each = nrow(mort3))
> C3 <- covMcd(mm)
> stopifnot(C3$mcd.wt == c3$mcd.wt)
> try(## error: with "old default tolerance:
+   covMcd(mm, control= rrcov.control(tol = 1e-10))
+ )
Error in solve.default(cov, ...) : 
  system is computationally singular: reciprocal condition number = 4.85293e-11
> 
> cat('Time elapsed: ', proc.time(),'\n') # for ``statistical reasons''
Time elapsed:  2.314 0.088 2.449 0 0 
> 
> ## "large" examples using different algo branches {seg.fault in version 0.4-4}:
> set.seed(1)
> 
> n <- 600 ## - partitioning will be triggered
> X <- matrix(round(100*rnorm(n * 3)), n, 3)
> cX <- covMcd(X)
> cX
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = X)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  25.1 
Robust Estimate of Location:
[1]   0.141  -6.083  -0.703
Robust Estimate of Covariance:
      [,1]   [,2]   [,3]
[1,]  9646   -114    389
[2,]  -114  11221    250
[3,]   389    250  11726
> n <- 2000 ## - nesting will be triggered
> X <- matrix(round(100*rnorm(n * 3)), n, 3)
> cX <- covMcd(X)
> cX
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = X)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  24.9 
Robust Estimate of Location:
[1]   0.201   1.455  -2.296
Robust Estimate of Covariance:
          [,1]  [,2]     [,3]
[1,]  10083.87   225     7.31
[2,]    224.92  9885   237.96
[3,]      7.31   238  9862.80
> 
> cat('Time elapsed: ', proc.time(),'\n')
Time elapsed:  2.549 0.09 2.686 0 0 
> 
> 
> ## Now, some small sample cases:
> 
> ## maximal values:
> n. <- 10
> p. <-  8
> set.seed(44)
> (X. <- cbind(1:n., round(10*rt(n.,3)), round(10*rt(n.,2)),
+              matrix(round(10*rnorm(n. * (p.-3)), 1),  nrow = n., ncol = p.-3)))
      [,1] [,2] [,3]  [,4]  [,5]  [,6] [,7]  [,8]
 [1,]    1    8    0  -3.6   4.7   3.0 -7.7  -3.3
 [2,]    2  -24    3   5.7 -15.6  13.5 -8.9 -10.0
 [3,]    3   -1    0  17.0  -1.9  19.0 17.4  -5.8
 [4,]    4   -9    2   0.1  -6.0 -11.5 18.6  25.8
 [5,]    5   -6  -31   2.4  10.0   9.6  5.4  -4.8
 [6,]    6    6   -3 -12.3  -4.6  17.2 -4.6  15.2
 [7,]    7   22   16  -2.8  -2.2  -5.2 -2.2   5.6
 [8,]    8   23    5  -9.0 -10.4  -2.6 -5.7   2.0
 [9,]    9    1   -9   2.1  -5.6   4.1  2.8  -3.0
[10,]   10  -17   -2  -8.8  -7.8   6.5  4.2  17.7
> 
> ## 2 x 1 ---> Error
> r <- try(covMcd(X.[1:2, 2, drop=FALSE]), silent=TRUE)
> stopifnot(inherits(r, "try-error"),
+           grep("too small sample size", r) == 1)
> 
> ## 3 x 2 --- ditto
> r <- try(covMcd(X.[1:3, 2:3]), silent=TRUE)
> stopifnot(inherits(r, "try-error"),
+           grep("too small sample size", r) == 1)
> 
> ## 5 x 3  [ n < 2 p  ! ]  --- also works for MASS
> X <- X.[1:5, 1:3]
> set.seed(101)
> ## the finite-sample correction is definitely doubtful:
> (cc <- covMcd(X, use.correction = FALSE))
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = X, use.correction = FALSE)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  4.30 
Robust Estimate of Location:
[1]   2.50  -6.50   1.25
Robust Estimate of Covariance:
        [,1]    [,2]     [,3]
[1,]   2.474   -6.93    0.742
[2,]  -6.928  273.67  -28.456
[3,]   0.742  -28.46    3.341
Warning message:
In covMcd(X, use.correction = FALSE) :
  n < 2 * p, i.e., possibly too small sample size
> str(cc) ## best = 2 3 4 5
List of 18
 $ method     : chr "Minimum Covariance Determinant Estimator."
 $ call       : language covMcd(x = X, use.correction = FALSE)
 $ cov        : num [1:3, 1:3] 2.474 -6.928 0.742 -6.928 273.675 ...
 $ center     : num [1:3] 2.5 -6.5 1.25
 $ n.obs      : int 5
 $ best       : int [1:4] 1 2 3 4
 $ alpha      : num 0.5
 $ quan       : num 4
 $ raw.cov    : num [1:3, 1:3] 2.474 -6.928 0.742 -6.928 273.675 ...
 $ raw.center : num [1:3] 2.5 -6.5 1.25
 $ raw.weights: num [1:5] 1 1 1 1 0
 $ crit       : num 73.3
 $ raw.mah    : num [1:5] 1.52 1.52 1.52 1.52 2724.44
 $ mah        : num [1:5] 1.52 1.52 1.52 1.52 2724.44
 $ mcd.wt     : num [1:5] 1 1 1 1 0
 $ X          : num [1:5, 1:3] 1 2 3 4 5 8 -24 -1 -9 -6 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:5] "1" "2" "3" "4" ...
  .. ..$ : NULL
 $ raw.cnp2   : num [1:2] 1.48 1
 $ cnp2       : num [1:2] 1.48 1
 - attr(*, "class")= chr "mcd"
> mcc <- MASS::cov.mcd(X)
> stopifnot(cc$best == mcc$best,
+           all.equal(cc$center, mcc$center, tol = 1e-10),
+           all.equal(c(mcc$cov / cc$raw.cov), rep(0.673549282206, 3*3)))
> 
> ## p = 4 -- 6 x 4 & 7 x 4  [ n < 2 p  ! ]
> p <- 4
> n <- 7
> X <- X.[1:n, 1+(1:p)]
> stopifnot(dim(X) == c(n,p))
> (cc <- covMcd(X, use.correction = FALSE))
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = X, use.correction = FALSE)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  15.6 
Robust Estimate of Location:
[1]   0.333   3.000   0.683  -4.267
Robust Estimate of Covariance:
       [,1]    [,2]     [,3]     [,4]
[1,]  319.0  61.163  -82.304  102.906
[2,]   61.2  57.565   -0.745   -0.874
[3,]  -82.3  -0.745  126.126  -15.035
[4,]  102.9  -0.874  -15.035   57.008
Warning message:
In covMcd(X, use.correction = FALSE) :
  n < 2 * p, i.e., possibly too small sample size
> str(cc) ## best = 1 2 4 5 6 7
List of 18
 $ method     : chr "Minimum Covariance Determinant Estimator."
 $ call       : language covMcd(x = X, use.correction = FALSE)
 $ cov        : num [1:4, 1:4] 319 61.2 -82.3 102.9 61.2 ...
 $ center     : num [1:4] 0.333 3 0.683 -4.267
 $ n.obs      : int 7
 $ best       : int [1:6] 1 2 3 4 6 7
 $ alpha      : num 0.5
 $ quan       : num 6
 $ raw.cov    : num [1:4, 1:4] 319 61.2 -82.3 102.9 61.2 ...
 $ raw.center : num [1:4] 0.333 3 0.683 -4.267
 $ raw.weights: num [1:7] 1 1 1 1 0 1 1
 $ crit       : num 6011409
 $ raw.mah    : num [1:7] 2.546 2.477 3.224 0.835 24.765 ...
 $ mah        : num [1:7] 2.546 2.477 3.224 0.835 24.765 ...
 $ mcd.wt     : num [1:7] 1 1 1 1 0 1 1
 $ X          : num [1:7, 1:4] 8 -24 -1 -9 -6 6 22 0 3 0 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:7] "1" "2" "3" "4" ...
  .. ..$ : NULL
 $ raw.cnp2   : num [1:2] 1.28 1
 $ cnp2       : num [1:2] 1.28 1
 - attr(*, "class")= chr "mcd"
> mcc <- MASS::cov.mcd(X)
> stopifnot(cc$best == mcc$best,
+           all.equal(cc$center, mcc$center, tol = 1e-10),
+           all.equal(c(mcc$cov / cc$raw.cov), rep(0.7782486992881, p*p)))
> n <- 6
> X <- X[1:n,]
> (cc <- covMcd(X, use.correction = FALSE))
Minimum Covariance Determinant (MCD) estimator.
Call:
covMcd(x = X, use.correction = FALSE)
-> Method:  Minimum Covariance Determinant Estimator. 

Log(Det.):  7.67 
Robust Estimate of Location:
[1]  -4.00   0.40   1.38  -4.68
Robust Estimate of Covariance:
       [,1]    [,2]   [,3]   [,4]
[1,]  225.1  -33.21  -76.3  115.1
[2,]  -33.2    7.04   17.1  -11.8
[3,]  -76.3   17.08  158.1  -16.6
[4,]  115.1  -11.83  -16.6   72.0
Warning message:
In covMcd(X, use.correction = FALSE) :
  n < 2 * p, i.e., possibly too small sample size
> mcc <- MASS::cov.mcd(X)
> stopifnot(cc$best == mcc$best,
+           all.equal(cc$center, mcc$center, tol = 1e-10),
+           all.equal(c(mcc$cov / cc$raw.cov), rep(0.7528695976179, p*p)))
> 
> cat('Time elapsed: ', proc.time(),'\n') # for ``statistical reasons''
Time elapsed:  2.611 0.098 2.755 0 0 
> 
> ## nsamp = "exact" -- here for p=7
> coleman.x <- data.matrix(coleman[, 1:6])
> system.time(CcX <- covMcd(coleman.x, nsamp="exact")) # ~ 3 sec.
Warning in .fastmcd(x, h, nsamp, trace = as.integer(trace)) :
  Computing all 77520 subsets of size 7 out of 20
 This may take a very long time!

   user  system elapsed 
  1.747   0.000   1.746 
> stopifnot(all.equal(CcX$best,
+                     c(2, 5:9, 11,13, 14:16, 19:20), tol=0))
>