Scale matrix estimation of an elliptically symmetric distribution in high and low dimensions

The problem of estimating the scale matrix ? in a multivariate additive model, with elliptical noise, is considered from decision-theoretic point view. As natural estimators form ˆ = S (where sample covariance and positive constant) perform poorly, we propose general , G ( + Z ) where Moore–Penrose inverse correction matrix. We provide conditions on such that improves over under quadratic loss L tr ? 1 I p 2 . adopt unified approach to two cases invertible singular. To this end, new Stein–Haff type identity calculus eigenstructure for are developed. Our theory illustrated large class which orthogonally invariant.