On the relation between S-Estimators and M-Estimators of multivariate location and covariance

Journal article (1989)

Authors

Faculty
Electrical Engineering, Mathematics and Computer Science (EEMCS) (TU Delft)
Copyright: © Institute of Mathematical Statistics
DOI: https://doi.org/doi:10.1214/aos/1176347386
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Published Date

1989

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Source:

Annals of statistics. 17(4)1989, 1662-1683

Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

We discuss the relation between S-estimators and M-estimators of multivariate location and covariance. As in the case of the estimation of a multiple regression parameter, S-estimators are shown to satisfy first-order conditions of M-estimators. We show that the influence function IF (x;S F) of S-functionals exists and is the same as that of corresponding M-functionals. Also, we show that S-estimators have a limiting normal distribution which is similar to the limiting normal distribution which is similar to the limiting normal distribution of M-estimators. Finally, we compare asymptotic variances and breakdown point of both types of estimators.