Journal of Applied Mathematics and Stochastic Analysis
Volume 5 (1992), Issue 2, Pages 167-175
doi:10.1155/S1048953392000145
Convergence rates for empirical Bayes two-action problems: the uniform U(0,θ)
distribution
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.
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.