Bayesian improvements of a MRE estimator of a bounded location parameter

Abstract

We study the frequentist risk performance of Bayesian estimators of a bounded location parameter, and focus on conditions placed on the shape of the prior density guaranteeing dominance over the minimum risk equivariant (MRE) estimator. For a large class of even and logconcave densities, even convex loss functions, we demonstrate in a unified manner that symmetric priors which are bowled shaped and logconcave lead to Bayesian dominating estimators. The results generalize similar results obtained by Marchand and Strawderman for the fully uniform prior, as well as those obtained by Kubokawa for squared error loss. Finally, we present a detailed example and several remarks.