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

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.