Convergence rates for empirical Bayes two-action problems: the uniform U(0, θ) distribution. (1992) - Tahir, Mohamed
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.