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On estimation of a matrix of normal means with unknown covariance matrix

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  • Konno, Yoshihiko
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    Abstract

    Let X be an m - p matrix normally distributed with matrix of means B and covariance matrix Im [circle times operator] [Sigma], where [Sigma] is a p - p unknown positive definite matrix. This paper studies the estimation of B relative to the invariant loss function tr . New classes of invariant minimax estimators are proposed for the case p > m + 1, which are multivariate extensions of the estimators of Stein and Baranchik. The method involves the unbiased estimation of the risk of an invariant estimator which depends on the eigenstructure of the usual F = XS-1Xt matrix, where S: p - p follows a Wishart matrix with n degrees of freedom and mean n[Sigma].

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    File URL: http://www.sciencedirect.com/science/article/B6WK9-4CTN8XK-G8/2/79cf07cdc6c4145fd36956ca480183d6
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 36 (1991)
    Issue (Month): 1 (January)
    Pages: 44-55

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    Handle: RePEc:eee:jmvana:v:36:y:1991:i:1:p:44-55

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    Related research

    Keywords: minimax estimation Stein estimator Baranchik-type estimator;

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    Cited by:
    1. Tatsuya Kubokawa & M. S. Srivastava, 2002. "Minimax Multivariate Empirical Bayes Estimators under Multicollinearity," CIRJE F-Series CIRJE-F-187, CIRJE, Faculty of Economics, University of Tokyo.
    2. Tsukuma, Hisayuki, 2010. "Shrinkage priors for Bayesian estimation of the mean matrix in an elliptically contoured distribution," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1483-1492, July.
    3. Kubokawa, T. & Srivastava, M. S., 2002. "Estimating Risk and the Mean Squared Error Matrix in Stein Estimation," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 39-64, July.
    4. Tatsuka Kubokawa & M. S. Srivastava, 2002. "Prediction in Multivariate Mixed Linear Models," CIRJE F-Series CIRJE-F-180, CIRJE, Faculty of Economics, University of Tokyo.
    5. Hisayuki Tsukuma & Tatsuya Kubokawa, 2005. "Methods for Improvement in Estimation of a Normal Mean Matrix," CIRJE F-Series CIRJE-F-378, CIRJE, Faculty of Economics, University of Tokyo.
    6. Tsukuma, Hisayuki, 2009. "Generalized Bayes minimax estimation of the normal mean matrix with unknown covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2296-2304, November.
    7. Tsukuma, Hisayuki, 2010. "Shrinkage minimax estimation and positive-part rule for a mean matrix in an elliptically contoured distribution," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 215-220, February.
    8. Kubokawa, T. & Srivastava, M. S., 2001. "Robust Improvement in Estimation of a Mean Matrix in an Elliptically Contoured Distribution," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 138-152, January.

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