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Hierarchical Empirical Bayes Estimation of Two Sample Means Under Divergence Loss

Author

Listed:
  • Malay Ghosh

    (University of Florida)

  • Tatsuya Kubokawa

    (University of Tokyo)

Abstract

We consider the problem of simultaneous estimation of two population means when one suspects that the two means are nearly equal. It is shown that the hierarchical empirical Bayes estimators which shrink the sample means towards the suspected hypothesis dominate the sample mean vectors in simultaneous estimation under the divergence loss function.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankha:v:80:y:2018:i:1:d:10.1007_s13171-018-0155-5
    DOI: 10.1007/s13171-018-0155-5
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    References listed on IDEAS

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    1. 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.
    2. Ghosh, Malay & Sinha, Bimal K., 1988. "Empirical and hierarchical bayes competitors of preliminary test estimators in two sample problems," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 206-227, October.
    3. 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.
    Full references (including those not matched with items on IDEAS)

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