Journal of Applied Mathematics and Stochastic Analysis
Volume 5 (1992), Issue 2, Pages 167-175

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

Mohamed Tahir

Temple University, Department of Statistics, Philadelphia 19122, PA, USA

Received 1 September 1991; Revised 1 December 1991

Copyright © 1992 Mohamed Tahir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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(nα), for some constant α, 0<α<1, where n is the number of accumulated past observations at hand.