Empirical Bayes Estimation of Binomial Parameter with Symmetric Priors

摘要

This paper deals with the problem of estimating the binomial parameter via the nonparametric empirical Bayes approach. This estimation problem has some surprising phenomenon that estimators which are asymptotically optimal in the usual empirical Bayes sense do not exist (Robbins (1956, 1964)). However, as pointed out by Liang (1984) and Gupta and Liang (1986), it is possible to construct asymptotically optimal empirical Bayes estimators if the unknown priors a monotone empirical Bayes estimator is constructed by using the isotonic regression method. This estimator is asymptotically optimal in the usual empirical Bayes sense. The corresponding rate of convergence is investigated and shown to be at least of order 1/n where n is the number of past observations at hand. (KR)