CHOICE OF HIERARCHICAL PRIORS - ADMISSIBILITY IN ESTIMATION OF NORMALMEANS

In hierarchical Bayesian modeling of normal means, it is common to com plete 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, ina dequate in the sense that estimators resulting from its use can be ina dmissible under quadratic loss. In this paper, hierarchical priors for normal means are categorized in terms of admissibility and inadmissib ility of resulting estimators for a quite general scenario. The Jeffre ys prior for the hypervariance and a shrinkage prior for the hypermean s are recommended as admissible alternatives. Incidental to this analy sis is presentation of the conditions under which the (generally impro per) priors result in proper posteriors.