On regularized general empirical Bayes estimation of normal means

In this paper we study a monotone regularized kernel general empirical Bayes method for the estimation of a vector of normal means. This estimator is used to improve upon the kernel methods of Zhang (1997) [12] and Brown and Greenshtein (2009) [5]. We prove an oracle inequality for the regret of the proposed estimator compared with the optimal Bayes risk. The oracle inequality leads to the property that the ratio of the proposed estimator to that of the Bayes procedure approaches one, under mild conditions. We demonstrate the performance of the estimator in simulation experiments with sparse and normal setups. It turns out that the proposed procedure indeed improves over its kernel version.