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Improved loss estimation for a normal mean matrix

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  • Matsuda, Takeru
  • Strawderman, William E.

Abstract

We investigate improved loss estimation in the matrix mean estimation problem. Specifically, for estimators of a normal mean matrix, we consider estimation of the Frobenius loss. Based on the singular values of the observation, we develop loss estimators that dominate the unbiased loss estimator for a broad class of matrix mean estimators including the Efron–Morris estimator. This is an extension of the results of Johnstone (1988) for a normal mean vector. We also provide improved estimators of loss for reduced-rank estimators. Numerical results show the effectiveness of the proposed loss estimators.

Suggested Citation

  • Matsuda, Takeru & Strawderman, William E., 2019. "Improved loss estimation for a normal mean matrix," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 300-311.
    • Handle: RePEc:eee:jmvana:v:169:y:2019:i:c:p:300-311
    DOI: 10.1016/j.jmva.2018.10.001
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    References listed on IDEAS

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    1. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2007. "Methods for improvement in estimation of a normal mean matrix," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1592-1610, September.
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    6. Aurélie Boisbunon & Stéphane Canu & Dominique Fourdrinier & William Strawderman & Martin T. Wells, 2014. "Akaike's Information Criterion, C p and Estimators of Loss for Elliptically Symmetric Distributions," International Statistical Review, International Statistical Institute, vol. 82(3), pages 422-439, December.
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    11. 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.
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    Cited by:

    1. Stéphane Canu & Dominique Fourdrinier, 2023. "Data based loss estimation of the mean of a spherical distribution with a residual vector," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(8), pages 851-878, November.

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