Let there be given a contaminated list of n R^d-valued observations coming
from g different, normally distributed populations with a common covariance
matrix. We compute the ML-estimator with respect to a certain statistical model
with n-r outliers for the parameters of the g populations; it detects outliers
and simultaneously partitions their complement into g clusters. It turns out
that the estimator unites both the minimum-covariance-determinant rejection
method and the well-known pooled determinant criterion of cluster analysis. We
also propose an efficient algorithm for approximating this estimator and study
its breakdown points for mean values and pooled SSP matrix.Comment: Published at http://dx.doi.org/10.1214/009053604000000940 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org