Shrinkage minimax estimation and positive-part rule for a mean matrix in an elliptically contoured distribution

Abstract

This paper addresses the problem of estimating the mean matrix of an elliptically contoured distribution with an unknown scale matrix. The unbiased estimator of the mean matrix is shown to be minimax relative to a quadratic loss. This fact yields minimaxity of a matricial shrinkage estimator improving on the unbiased estimator. A positive-part rule for eigenvalues of matricial shrinkage factor provides a better estimator than the shrinkage minimax one.