The Annals of Statistics

Choice of hierarchical priors: admissibility in estimation of normal means

James O. Berger and William E. Strawderman

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 20 September 2002

Permanent link to this document
http://projecteuclid.org/euclid.aos/1032526950

Digital Object Identifier
doi:10.1214/aos/1032526950

Mathematical Reviews number (MathSciNet)
MR1401831

Zentralblatt MATH identifier
0865.62004

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

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

Citation

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. http://projecteuclid.org/euclid.aos/1032526950.


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