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Hierarchical Empirical Bayes Estimation of Two Sample Means Under Divergence Loss

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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.

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Acknowledgments

The authors are grateful to the Editor, the Associate Editor and two reviewers for their valuable comments and helpful suggestions. Research of the second author was supported in part by Grant-in-Aid for Scientific Research (15H01943 and 26330036) from Japan Society for the Promotion of Science.

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Authors and Affiliations

  1. Department of Statistics, University of Florida, 102 Griffin-Floyd Hall, Gainesville, FL, 32611, USA

    Malay Ghosh

  2. Faculty of Economics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Tatsuya Kubokawa

Authors
  1. Malay Ghosh
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  2. Tatsuya Kubokawa
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Correspondence to Malay Ghosh.

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Ghosh, M., Kubokawa, T. Hierarchical Empirical Bayes Estimation of Two Sample Means Under Divergence Loss. Sankhya A 80 (Suppl 1), 70–83 (2018). https://doi.org/10.1007/s13171-018-0155-5

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  • DOI: https://doi.org/10.1007/s13171-018-0155-5

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