Empirical Bayes Estimation With Kernel Sequence Method

摘要

In this paper, we consider the empirical Bayes estimation in the exponential family. A minimax lower bound is derived. It is shown that the best possible rate of empirical Bayes estimators is O(1/n) if Theta is bounded. Then we turn to find an empirical Bayes estimator with a rate close to this lower bound rate. Applying the kernel sequence method, we are able to construct an empirical Bayes estimator with a rate of O(1/n(1n n)7(1n 1n n)2). Under the same assumption, this rate is the fastest compared to the earlier results published in the literature.