Characterization of Priors in the Stein Problem

Tatsuya Kubokawa
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Tatsuya Kubokawa: Faculty of Economics, University of Tokyo

No CIRJE-F-409, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

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.

Pages: 35pages
Date: 2006-03
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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2006cf409

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