On Bayes minimax estimators for a normal mean with an uncertain constraint†

Abstract

We describe a hierarchical Bayesian approach for inference about a parameter θ lower-bounded by α with uncertain α, derive some basic identities for posterior analysis about , and provide illustrations for normal and Poisson models. For the normal case with unknown mean θ and known variance , we obtain Bayes estimators of θ that take values on , but that are equally adapted to a lower-bound constraint in being minimax under squared error loss for the constrained problem.