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On minimaxity and admissibility of hierarchical Bayes estimators

Author

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  • Kubokawa, Tatsuya
  • Strawderman, William E.

Abstract

This paper obtains conditions for minimaxity of hierarchical Bayes estimators in the estimation of a mean vector of a multivariate normal distribution. Hierarchical prior distributions with three types of second stage priors are treated. Conditions for admissibility and inadmissibility of the hierarchical Bayes estimators are also derived using the arguments in Berger and Strawderman [Choice of hierarchical priors: admissibility in estimation of normal means, Ann. Statist. 24 (1996) 931-951]. Combining these results yields admissible and minimax hierarchical Bayes estimators.

Suggested Citation

  • Kubokawa, Tatsuya & Strawderman, William E., 2007. "On minimaxity and admissibility of hierarchical Bayes estimators," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 829-851, April.
    • Handle: RePEc:eee:jmvana:v:98:y:2007:i:4:p:829-851
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    Citations

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    Cited by:

    1. Tatsuya Kubokawa & William E. Strawderman, 2011. "Admissibility and Minimaxity of Benchmarked Shrinkage Estimators," CIRJE F-Series CIRJE-F-809, CIRJE, Faculty of Economics, University of Tokyo.
    2. Nakada, Ryumei & Kubokawa, Tatsuya & Ghosh, Malay & Karmakar, Sayar, 2021. "Shrinkage estimation with singular priors and an application to small area estimation," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    3. Tsukuma, Hisayuki, 2008. "Admissibility and minimaxity of Bayes estimators for a normal mean matrix," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2251-2264, November.

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