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.