Language Reference

Consider the Brownlee (1965) stackloss data used in the example for the MVE subroutine.

For and (three explanatory variables including intercept), you obtain a total of 5,985 different subsets of 4 observations out of 21. If you decide not to specify opt[5], the MCD algorithm chooses 500 random sample subsets, as in the following statements:

   /* Int X1  X2  X3   Y  Stackloss data */
aa = { 1  80  27  89  42,
       1  80  27  88  37,
       1  75  25  90  37,
       1  62  24  87  28,
       1  62  22  87  18,
       1  62  23  87  18,
       1  62  24  93  19,
       1  62  24  93  20,
       1  58  23  87  15,
       1  58  18  80  14,
       1  58  18  89  14,
       1  58  17  88  13,
       1  58  18  82  11,
       1  58  19  93  12,
       1  50  18  89   8,
       1  50  18  86   7,
       1  50  19  72   8,
       1  50  19  79   8,
       1  50  20  80   9,
       1  56  20  82  15,
       1  70  20  91  15 };

a = aa[,2:4];            /* X1-X3 */
opt = j(8, 1, .);
opt[1] = 2;              /* ipri */
opt[2] = 1;              /* pcov: print COV */
opt[3] = 1;              /* pcor: print CORR */

call mcd(sc, xmcd, dist, opt, a);

A portion of the output is shown in the following figures. Figure 250 shows a summary of the MCD algorithm and the final h points selected.

Figure 251 shows the observations that were chosen that are used to form the robust estimates.

Figure 252 shows the MCD estimators of the location, scatter matrix, and correlation matrix. The MCD scatter matrix is multiplied by a factor to make it consistent with the data that come from a single Gaussian distribution.

Figure 253 shows the classical Mahalanobis distances, the robust distances, and the weights that identify the outlying observations (that is, leverage points when explaining y with these three regressor variables).