Bayesian input in Stein estimation and a new minimax empirical Bayes estimator

The relationship between Stein estimation of a multivariate normal mean and Bayesian analysis is considered. The necessity to involve prior information is discussed, and the various methods of so doing are reviewed. These include direct Bayesian analyses, ad hoc utilization of prior information, restricted class Bayesian and Γ-minimax analyses, and Type II maximum likelihood (empirical Bayes) methods. A new empirical Bayes Stein-type estimator is developed, via the latter method, for an interesting ε{lunate}-contamination class of priors, and is shown to be minimax under reasonable conditions. The minimax proof contains some novel theoretical features. © 1984.

Duke Scholars

Author James O. Berger Statistical Science