Qualitative Robustness of S*‐estimators of Multivariate Location and Dispersion

In: Statistica Neerlandica: journal of the Netherlands Society for Statistics and Operations Research, Band 51, Heft 3, S. 257-268

Abstract

S‐estimators of multivariate location and dispersion are favored for their robustness against outliers. The computations of the exact S‐estimators, however, are difficult, if not impossible. We consider S*‐estimators, a variant of the S‐estimators which is commonly computed in reality. It is shown under very general conditions that S*‐estimators are qualitatively robust with respect to a wide range of metrics, including Prohorov metric and a weak affine invariant metric based on Vapnik‐Cervonenkis sets. The result follows from a continuity result of the S*‐functionals and almost everywhere continuity result of the corresponding estimators in finite‐sample cases.