Orthogonal Equivariant Minimax Estimatorsof Bivariate Normal Covariance Matrix and Precision Matrix

Abstract

The scale and orthogonal equivariant minimax estimators are obtained for the bivariate normal covariance matrix and precision matrix under Selliah's (1964} and Stein's (1961) loss functions. These new estimators are better than Selliah's and Stein's minimax estimators. An unbiased estimator of the risk of the new estimator is obtained under Selliah's loss function using Haff's (1979) identity for the Wishart distribution. Simulation results seem to indicate that the new estimators dominate the corresponding Hatf's [(1979), (1980)] estimators. We also prove that, for p-2, Haff's estimators are not minimax.