Influence function and efficiency of the minimum covariance determinant scatter matrix estimator

The minimum covariance determinant (MCD) scatter estimator is a highly robust estimator for the dispersion matrix of a multivariate, elliptically symmetric distribution. It is relatively fast to compute and intuitively appealing. In this note we derive its influence function and compute the asymptotic variances of its elements. A comparison with the one step reweighted MCD and with S-estimators is made. Also finite-sample results are reported. (C) 1999 Academic Press AMS 1991 subject classifications: 62F35, 62G35.