Improved estimation of the covariance matrix under Stein's loss

Ren-Dao Ye and Song-Gui Wang

Statistics & Probability Letters, 2009, vol. 79, issue 6, 715-721

Abstract: 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 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 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.

Keywords: primary; 62H12 secondary; 62J10 (search for similar items in EconPapers)
Date: 2009
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