#### Choice of Hierarchical Priors: Admissibility in Estimation
Of Normal Means

James Berger and William Strawderman

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 hyper-variance and a shrinkage prior for the hyper-means
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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