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December 1998 Minimax bias-robust estimation of the dispersion matrix of a multivariate distribution
Jorge G. Adrover
Ann. Statist. 26(6): 2301-2320 (December 1998). DOI: 10.1214/aos/1024691472

Abstract

Maronna defines affine equivariant $M$-estimators for multivariate location and scatter. They are particularly suited for estimating the pseudo-covariance or scatter matrix of an elliptical population. By defining the bias of a dispersion matrix properly, we consider the maximum bias of an $M$-estimator over an $\varepsilon$ -neighborhood of the underlying elliptical distribution (location known). We find that Tyler’s estimator minimizes the maximum bias.

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Jorge G. Adrover. "Minimax bias-robust estimation of the dispersion matrix of a multivariate distribution." Ann. Statist. 26 (6) 2301 - 2320, December 1998. https://doi.org/10.1214/aos/1024691472

Information

Published: December 1998
First available in Project Euclid: 21 June 2002

zbMATH: 0927.62054
MathSciNet: MR1700233
Digital Object Identifier: 10.1214/aos/1024691472

Subjects:
Primary: 62H10, 62H12
Secondary: 62G05

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 6 • December 1998
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