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December, 1989 On the Relation between $S$-Estimators and $M$-Estimators of Multivariate Location and Covariance
Hendrik P. Lopuhaa
Ann. Statist. 17(4): 1662-1683 (December, 1989). DOI: 10.1214/aos/1176347386

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 $(\mathbf{x; S}, F)$ 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.

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Hendrik P. Lopuhaa. "On the Relation between $S$-Estimators and $M$-Estimators of Multivariate Location and Covariance." Ann. Statist. 17 (4) 1662 - 1683, December, 1989. https://doi.org/10.1214/aos/1176347386

Information

Published: December, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0702.62031
MathSciNet: MR1026304
Digital Object Identifier: 10.1214/aos/1176347386

Subjects:
Primary: 62F35
Secondary: 62H12

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 4 • December, 1989
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