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On the Stein phenomenon under divergence loss and an unknown variance-covariance matrix

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  • Ghosh, Malay
  • Mergel, Victor

Abstract

The paper develops a general class of shrinkage estimators for estimating the normal mean, which dominates the sample mean in three or higher dimensions under a general divergence loss. In the process, the earlier works of James and Stein [11] and Efron and Morris [5] are generalized considerably.

Suggested Citation

  • Ghosh, Malay & Mergel, Victor, 2009. "On the Stein phenomenon under divergence loss and an unknown variance-covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2331-2336, November.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:10:p:2331-2336
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    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(09)00066-9
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    References listed on IDEAS

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    1. Ghosh, Malay & Mergel, Victor & Datta, Gauri Sankar, 2008. "Estimation, prediction and the Stein phenomenon under divergence loss," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1941-1961, October.
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    Cited by:

    1. Malay Ghosh & Tatsuya Kubokawa, 2018. "Hierarchical Empirical Bayes Estimation of Two Sample Means Under Divergence Loss," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 70-83, December.

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    1. Malay Ghosh & Tatsuya Kubokawa & Gauri Sankar Datta, 2020. "Density Prediction and the Stein Phenomenon," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 330-352, August.
    2. Malay Ghosh & Tatsuya Kubokawa, 2018. "Hierarchical Empirical Bayes Estimation of Two Sample Means Under Divergence Loss," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 70-83, December.

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