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2015 $M$-functionals of multivariate scatter
Lutz Dümbgen, Markus Pauly, Thomas Schweizer
Statist. Surv. 9: 32-105 (2015). DOI: 10.1214/15-SS109

Abstract

This survey provides a self-contained account of $M$-estimation of multivariate scatter. In particular, we present new proofs for existence of the underlying $M$-functionals and discuss their weak continuity and differentiability. This is done in a rather general framework with matrix-valued random variables. By doing so we reveal a connection between Tyler’s (1987a) $M$-functional of scatter and the estimation of proportional covariance matrices. Moreover, this general framework allows us to treat a new class of scatter estimators, based on symmetrizations of arbitrary order. Finally these results are applied to $M$-estimation of multivariate location and scatter via multivariate $t$-distributions.

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Lutz Dümbgen. Markus Pauly. Thomas Schweizer. "$M$-functionals of multivariate scatter." Statist. Surv. 9 32 - 105, 2015. https://doi.org/10.1214/15-SS109

Information

Published: 2015
First available in Project Euclid: 20 March 2015

zbMATH: 1309.62087
MathSciNet: MR3324616
Digital Object Identifier: 10.1214/15-SS109

Subjects:
Primary: 62G20, 62G35, 62H12, 62H99

Rights: Copyright © 2015 The author, under a Creative Commons Attribution License

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