Asymptotic risk comparison of some estimators for bivariate normal covariance matrix

Abstract

For Selliah's [5] and Stein's [3] loss functions, Sharmaand Krishnamoorthy [6] have considered orthogonal equivariant estimators $\Psi$. In this paper, we obtain asymptotic risk expressions for $\Psi$ and make a numerical comparison with those for Haff's [2] and Sugiura-Fujimoto [7] estimators. It is observed that $\Psi$ is uniformly better than Haff's estimator and better than Sugiura-Fujimoto estimator except in a small region of the parameter space.