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On minimaxity and admissibility of hierarchical Bayes estimators

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  • Kubokawa, Tatsuya
  • Strawderman, William E.
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 4 (April)
    Pages: 829-851

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:4:p:829-851

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    Related research

    Keywords: Admissibility Bayes inference Estimation Hierarchical Bayes model Inadmissibility Minimaxity Mixed linear model Multivariate normal distribution Shrinkage estimation;

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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. 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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