The largest nonidentifiable outlier: A comparison of multivariate simultaneous outlier identification rules

The aim of detecting outliers in a multivariate sample can be pursued in different ways. We investigate here the performance of several simultaneous multivariate outlier identification rules based on robust estimators of location and scale. It has been shown that the use of estimators with high finite sample breakdown point in such procedures yields a good behaviour with respect to the prevention of breakdown by the masking effect (Becker, Gather 1999, J. Amer. Statist. Assoc. 94, 947-955). In this article, we investigate by simulation, at which distance from the center of an underlying model distribution outliers can be placed until certain simultaneous identification rules will detect them as outliers. We consider identification procedures based on the minimum volume ellipsoid, the minimum covariance determinant, and S-estimators.