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June 1996 Choice of hierarchical priors: admissibility in estimation of normal means
James O. Berger, William E. Strawderman
Ann. Statist. 24(3): 931-951 (June 1996). DOI: 10.1214/aos/1032526950


In hierarchical Bayesian modeling of normal means, it is common to complete the prior specification by choosing a constant prior density for unmodeled hyperparameters (e.g., variances and highest-level means). This common practice often results in an inadequate overall prior, inadequate in the sense that estimators resulting from its use can be inadmissible under quadratic loss. In this paper, hierarchical priors for normal means are categorized in terms of admissibility and inadmissibility of resulting estimators for a quite general scenario. The Jeffreys prior for the hypervariance and a shrinkage prior for the hypermeans are recommended as admissible alternatives. Incidental to this analysis is presentation of the conditions under which the (generally improper) priors result in proper posteriors.


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James O. Berger. William E. Strawderman. "Choice of hierarchical priors: admissibility in estimation of normal means." Ann. Statist. 24 (3) 931 - 951, June 1996.


Published: June 1996
First available in Project Euclid: 20 September 2002

zbMATH: 0865.62004
MathSciNet: MR1401831
Digital Object Identifier: 10.1214/aos/1032526950

Primary: 62F15
Secondary: 62C15 , 62C20 , 62J07

Keywords: hyperparameters , inadmissibility , mean-squared error , Normal hierarchical models , shrinkage estimation

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 3 • June 1996
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