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Weighted shrinkage estimators of normal mean matrices and dominance properties

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  • Yuasa, Ryota
  • Kubokawa, Tatsuya

Abstract

In the estimation of the mean matrix in a multivariate normal distribution, the Efron–Morris estimator and the James–Stein estimator are two well-known minimax procedures, where the former is matricial shrinkage and the latter is scalar shrinkage. The methods for combining the two estimators with random weight functions are addressed. For deriving weight functions, the paper suggests the two methods. One is the minimization of a part of the unbiased estimator of the risk function, and the other is the empirical Bayes approach. The resulting weighted shrinkage estimators are shown to be minimax, and the extension to the case of an unknown covariance matrix is developed.

Suggested Citation

  • Yuasa, Ryota & Kubokawa, Tatsuya, 2023. "Weighted shrinkage estimators of normal mean matrices and dominance properties," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:jmvana:v:194:y:2023:i:c:s0047259x22001294
    DOI: 10.1016/j.jmva.2022.105138
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
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