Asymptotic risk comparison of some estimators for bivariate normal covariance matrix (Q1059954)

For \textit{J. S. Selliah}'s [Estimation and testing problems in Wishart distribution. Tech. Rep. 10, Stanford Univ. (1964)] and Stein's [cf. \textit{W. James} and \textit{C. Stein}, Estimation with quadratic loss. Proc. 4th Berkeley Sympos. math. statist. Probab. 1, 361-379 (1961)] loss functions, the authors [Orthogonal equivariant minimax estimators of bivariate normal covariance matrix and precision matrix. Bull., Calcutta Stat. Assoc. 32, 23-45 (1983)] have considered orthogonal equivariant estimators \(\Psi\). In this paper, they obtain asymptotic risk expressions for \(\Psi\) and make a numerical comparison with those for \textit{L. R. Haff}'s [Ann. Stat. 8, 586-597 (1980; Zbl 0441.62045)] and \textit{N. Sugiura} and \textit{M. Fujimoto} [Tsukuba Math. J. 6, 103-126 (1982; Zbl 0531.62054)] 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.