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Zbl 0865.62004
Berger, James O.; Strawderman, William E.
Choice of hierarchical priors: Admissibility in estimation of normal means. (English)
[J] Ann. Stat. 24, No.3, 931-951 (1996). ISSN 0090-5364

Summary: 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.\par 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.

MSC 2000:: *62C15 statistical admissibility
62F15 Bayesian inference
62H12 Multivariate estimation

Keywords: hyperparameters; mean-squared error; shrinkage estimation; improper priors; hierarchical Bayesian modeling of normal means; hierarchical priors for normal means; inadmissibility; Jeffreys prior; hypervariance; shrinkage prior; hypermeans; proper posteriors

Cited in: Zbl 1118.62034

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