Improved estimation of the covariance matrix under Stein’s loss

In this paper, the problem of estimating the covariance matrix of a multivariate normal population is considered. Some new classes of orthogonally invariant minimax estimators which include random mixtures of the modified estimators of ΣˆDS proposed by Dey and Srinivasan [Dey, D.K., Srinivasan, C., 1985. Estimation of a covariance matrix under Stein’s loss. Ann. Statist. 13, 1581–1591] and the identity matrix are proposed. It is shown that the new estimators dominate the modified estimators of ΣˆDS under Stein’s loss. Moreover, the ordering property of our classes of estimators is satisfied. Finally, the inadmissibility of the order-preserving minimax estimators is obtained.