On the Convergence Rates of Empirical Bayes Rules for Two-Action Problems. Discrete Case.
PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS
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The purpose of this paper is to investigate the convergence rates of a sequence of empirical Bayes decision rules for the two-action decision problems where the distributions of the observations belong to a discrete exponential family. It is found that the sequence of the empirical Bayes decision rules under study is asymptotically optimal, and the order of associated convergence rates is Oexp-cn, for some positive constant c, where n is the number of accumulated past experience observations at hand. Two examples are provided to illustrate the performance of the proposed empirical Bayes decision rules. A comparison is also made between the proposed empirical Bayes rules and some earlier existng empirical Bayes rules.
- Statistics and Probability