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Characterization of Priors in the Stein Problem

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  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)

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    Abstract

    The so-called Stein problem is addressed in the estimation of a mean vector of a multivariate normal distribution with a known covariance matrix. For general prior distributions with sphericity, the paper derives conditions on priors under which the resulting generalized Bayes estimators are minimax. It is also shown that the conditions can be expressed based on the inverse Laplace transform of the general prior. The relationsip between Stein's super-harmonic condition and the general conditions is discussed. Finally, a characterization of the priors for the admissibility is given, and admissible and minimax estimators are developed.

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    Bibliographic Info

    Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-409.

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    Length: 35pages
    Date of creation: Mar 2006
    Date of revision:
    Handle: RePEc:tky:fseres:2006cf409

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