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Qualitative Robustness of S*‐estimators of Multivariate Location and Dispersion
Author(s) -
He X.,
Wang G.
Publication year - 1997
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/1467-9574.00054
Subject(s) - estimator , mathematics , outlier , affine transformation , robustness (evolution) , m estimator , computation , invariant (physics) , multivariate statistics , multivariate normal distribution , statistics , algorithm , geometry , biochemistry , chemistry , mathematical physics , gene
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.