The Annals of Statistics

Choice of hierarchical priors: admissibility in estimation of normal means

James O. Berger and William E. Strawderman

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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.

Article information

Ann. Statist. Volume 24, Number 3 (1996), 931-951.

First available in Project Euclid: 20 September 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F15: Bayesian inference
Secondary: 62C15: Admissibility 62C20: Minimax procedures 62J07: Ridge regression; shrinkage estimators

Normal hierarchical models hyperparameters inadmissibility mean-squared error shrinkage estimation


Berger, James O.; Strawderman, William E. Choice of hierarchical priors: admissibility in estimation of normal means. Ann. Statist. 24 (1996), no. 3, 931--951. doi:10.1214/aos/1032526950.

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