Bayesian improvements of a MRE estimator under general convex loss functions

Bayesian improvements of a MRE estimator under general convex loss functions

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 log.concave 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 Straw derman 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.