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Shrinkage minimax estimation and positive-part rule for a mean matrix in an elliptically contoured distribution

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  • Tsukuma, Hisayuki

Abstract

This paper addresses the problem of estimating the mean matrix of an elliptically contoured distribution with an unknown scale matrix. The unbiased estimator of the mean matrix is shown to be minimax relative to a quadratic loss. This fact yields minimaxity of a matricial shrinkage estimator improving on the unbiased estimator. A positive-part rule for eigenvalues of matricial shrinkage factor provides a better estimator than the shrinkage minimax one.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:3-4:p:215-220
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    References listed on IDEAS

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    1. 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.
    2. Konno, Yoshihiko, 1991. "On estimation of a matrix of normal means with unknown covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 36(1), pages 44-55, January.
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    Cited by:

    1. Yuasa, Ryota & Kubokawa, Tatsuya, 2023. "Weighted shrinkage estimators of normal mean matrices and dominance properties," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    2. Hisayuki Tsukuma & Tatsuya Kubokawa, 2014. "A Unified Approach to Estimating a Normal Mean Matrix in High and Low Dimensions," CIRJE F-Series CIRJE-F-926, CIRJE, Faculty of Economics, University of Tokyo.
    3. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2015. "A unified approach to estimating a normal mean matrix in high and low dimensions," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 312-328.
    4. Yuasa, Ryota & Kubokawa, Tatsuya, 2020. "Ridge-type linear shrinkage estimation of the mean matrix of a high-dimensional normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 178(C).

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