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Improved estimation of the covariance matrix under Stein's loss

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  • Ye, Ren-Dao
  • Wang, Song-Gui

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.

Suggested Citation

  • Ye, Ren-Dao & Wang, Song-Gui, 2009. "Improved estimation of the covariance matrix under Stein's loss," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 715-721, March.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:6:p:715-721
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    References listed on IDEAS

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    1. Sheena, Yo & Takemura, Akimichi, 1992. "Inadmissibility of non-order-preserving orthogonally invariant estimators of the covariance matrix in the case of Stein's loss," Journal of Multivariate Analysis, Elsevier, vol. 41(1), pages 117-131, April.
    2. Pui Leung & Wai Chan, 1998. "Estimation of the Scale Matrix and its Eigenvalues in the Wishart and the Multivariate F Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(3), pages 523-530, September.
    3. Leung, Pui Lam & Ng, Foon Yip, 2004. "Improved estimation of a covariance matrix in an elliptically contoured matrix distribution," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 131-137, January.
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