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Inadmissibility of non-order-preserving orthogonally invariant estimators of the covariance matrix in the case of Stein's loss

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  • Sheena, Yo
  • Takemura, Akimichi

Abstract

For orthogonally invariant estimation of [Sigma] of Wishart distribution using Stein's loss, any estimator which does not preserve the order of the sample eigenvalues is dominated by a modified estimator preserving the order.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:41:y:1992:i:1:p:117-131
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    Citations

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    Cited by:

    1. Konno, Yoshihiko, 2007. "Estimation of normal covariance matrices parametrized by irreducible symmetric cones under Stein's loss," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 295-316, February.
    2. Tatsuya Kubokawa & M. S. Srivastava, 1999. ""Estimating the Covariance Matrix: A New Approach", June 1999," CIRJE F-Series CIRJE-F-52, CIRJE, Faculty of Economics, University of Tokyo.
    3. Kubokawa, T. & Srivastava, M. S., 2003. "Estimating the covariance matrix: a new approach," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 28-47, July.
    4. Tatsuya Kubokawa, 2004. "A Revisit to Estimation of the Precision Matrix of the Wishart Distribution," CIRJE F-Series CIRJE-F-264, CIRJE, Faculty of Economics, University of Tokyo.
    5. Satoshi Kuriki, 1993. "Orthogonally invariant estimation of the skew-symmetric normal mean matrix," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(4), pages 731-739, December.
    6. 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.
    7. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2011. "Modifying estimators of ordered positive parameters under the Stein loss," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 164-181, January.
    8. Konno, Yoshihiko, 2001. "Inadmissibility of the Maximum Likekihood Estimator of Normal Covariance Matrices with the Lattice Conditional Independence," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 33-51, October.
    9. Sheena Yo & Gupta Arjun K., 2003. "Estimation of the multivariate normal covariance matrix under some restrictions," Statistics & Risk Modeling, De Gruyter, vol. 21(4), pages 327-342, April.
    10. Takemura, Akimichi & Sheena, Yo, 2005. "Distribution of eigenvalues and eigenvectors of Wishart matrix when the population eigenvalues are infinitely dispersed and its application to minimax estimation of covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 271-299, June.
    11. Tsai, Ming-Tien & Kubokawa, Tatsuya, 2007. "Estimation of Wishart mean matrices under simple tree ordering," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 945-959, May.
    12. Tsukuma, Hisayuki, 2016. "Estimation of a high-dimensional covariance matrix with the Stein loss," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 1-17.
    13. Tsukuma, Hisayuki, 2008. "Admissibility and minimaxity of Bayes estimators for a normal mean matrix," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2251-2264, November.
    14. Perron, François, 1997. "On a Conjecture of Krishnamoorthy and Gupta, ," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 110-120, July.
    15. Tatsuya Kubokawa & M. S. Srivastava, 2002. "Estimating the Covariance Matrix: A New Approach," CIRJE F-Series CIRJE-F-162, CIRJE, Faculty of Economics, University of Tokyo.
    16. Sheena, Yo & Takemura, Akimichi, 2008. "Asymptotic distribution of Wishart matrix for block-wise dispersion of population eigenvalues," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 751-775, April.
    17. Besson, Olivier & Vincent, François & Gendre, Xavier, 2020. "A Stein’s approach to covariance matrix estimation using regularization of Cholesky factor and log-Cholesky metric," Statistics & Probability Letters, Elsevier, vol. 167(C).
    18. Bodnar, Olha & Bodnar, Taras & Parolya, Nestor, 2022. "Recent advances in shrinkage-based high-dimensional inference," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    19. Hara, Hisayuki, 2001. "Other Classes of Minimax Estimators of Variance Covariance Matrix in Multivariate Normal Distribution," Journal of Multivariate Analysis, Elsevier, vol. 77(2), pages 175-186, May.

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