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 di erent ways We investigate here the performance of several simultaneous multivariate outlier identi cation rules based on robust estimators of location and scale It has been shown that the use of estimators with high nite sample breakdown point in such procedures yields a good behaviour with respect to the prevention of breakdown by the masking e ect Becker Gather J Amer Statist Assoc 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 identi cation rules will detect them as outliers We consider identi cation procedures based on the minimum volume ellipsoid the minimum covariance determinant and S estimators