Discrete density smoothing applied to the empirical bayes estimation of a poission mean

In the Empirical Bayes (EB) approach to estimating the mean of a Poission distribution, smoothing procedures are required to improve the performance of an EB estimator in small samples. Various smooth EB estimators in the literature strongly deopend on the nondecreasing property of the Bayes estimator when a priori gamma density is assumed. Such EB estimators provide good small sample properties but fail to have for general priors the asymptotic optimality property as defined by Robbins (1964). In this paper various smoothed estimators of a discrete density are introduced and applied to this EB problem. The resulting EB estimators are asymptotically optimal. Based on simulation with a gamma prior, they perform rather poorly as compared to other smooth EB rules in small samples and thus in not practical in the small sample environment. However, they are uniformly better than Robbins' estimator and better than the classical MVU estimator in most cases, while retaining the property of asymptotic optimality which those based on a gamma prior do not have.