The Annals of Statistics

Minimax bias-robust estimation of the dispersion matrix of a multivariate distribution

Jorge G. Adrover

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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.

Article information

Ann. Statist., Volume 26, Number 6 (1998), 2301-2320.

First available in Project Euclid: 21 June 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62H12: Estimation 62H10
Secondary: 62G05: Estimation

Bias covariance matrix elliptical distribution $M$-estimation mini-max estimation multivariate scatter pseudocovariance matrix robustness


Adrover, Jorge G. Minimax bias-robust estimation of the dispersion matrix of a multivariate distribution. Ann. Statist. 26 (1998), no. 6, 2301--2320. doi:10.1214/aos/1024691472.

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