On the attainment of a lower bound for the bates risk in estimating a parametric function

Abstract

A variation of a BAYESian analogue to the RAO-CRAMER Inequality Is examined under the assumption of a quadratic loss function for extimating some function τ(θ) of a real-valued parameter θ A necessary and sufficient condition under which the BAYES estimator attains the lower bound for the BAYES risk provided by the inequality is given when the posterior density is of the exponential type. As application an inequality involving gamma functions Is then derived