ON MINIMAXITY OF SOME ORTHOGONALLY INVARIANT ESTIMATORS OF BIVARIATE NORMAL DISPERSION MATRIX

Abstract

We consider an orthogonally invariant estimation of Σ of Wishart distribution using Stein’s loss (entropy loss) or a quadratic loss. In these problems the best lower triangular matrix invariant estimators are minimax estimators. Some orthogonally invariant estimators were derived from those minimax estimators. It is conjectured that they are also minimax estimators, but some estimators have not yet been proved to be minimax. In this paper we prove the minimaxity of some estimators when the dimension is two. We also present the necessary conditions for a class of estimators to be minimax when the dimension is two.