UNBIASED ESTIMATOR OF RISK FOR AN ORTHOGONALLY INVARIANT ESTIMATOR OF A COVARIANCE MATRIX

Abstract

The problem of estimating a covariance matrix in a multivariate normal distribution is discussed. A proof to derive the unbiased estimator of the risk of an orthogonally invariant estimator is given for Stein's loss function and a quadratic loss function. The range of applicable estimator is more clearly described compared to previous literature, and a new interpretation of Stein's estimator is referred to as an application.