Bayes estimation with spherically symmetric,convex loss

Summary It is desired to estimate a parameter with the loss function of the formL(θ, a)=W(‖θ−a‖), where is convex, differentiable, and non-decreasing. With this structure a characterization of Bayes estimators is given. Also it is noted that if the sample space, , for the observation,X, is a complete separable metric space then a Bayes estimator exists.