Convergence rates for empirical Bayes two-action problems: the uniform U(0,θ) distribution

Abstract

The purpose of this paper is to study the convergence rates of a sequence of empirical Bayes decision rules for the two-action problems in which the observations are uniformly distributed over the interval (0,θ), where θ is a value of a random variable having an unknown prior distribution. It is shown that the proposed empirical Bayes decision rules are asymptotically optimal and that the order of associated convergence rates is O(n−α), for some constant α, 0<α<1, where n is the number of accumulated past observations at hand.