Let ????̂ and ????̂ be the MCD estimators of location and scatter, which minimize the scale ????̂(d1, ...dn) = ∑h i=1 d(i). For each subsample A = {xi1

, .., , xih

} of size h call xA and CA the sample mean and covariance matrix corresponding to A. Let A∗ be a subsample of size h that minimizes |CA|. Show that A∗ is the set of observations corresponding to the h smallest values d(xi, ????̂, ????̂), and that

????̂ = xA∗ and ????̂ = |CA∗ |

−1∕pCA∗ .