Inadmissibility of Non-Order-Preserving Orthogonally Invariant Estimators of the Precision Matrix under Stein's Loss

Abstract

We consider orthogonally invariant estimation of Σ^-1 of a Wishart distribution using Stein's loss. We prove that any estimator which does not preserve the order of the eigenvalues of W -1 is dominated by a modified estimator preserving the order for the case p=2, 3.