On Regularized Empirical Bayes Estimation Of Normal Means

In this paper we study a regularized kernel general empirical Bayes method for theestimation of a vector of normal means. This estimator is used to improve upon thenormal kernel methods of Brown and Greenshtein (2009)§which is inspired by Jiang(2013).And the adaptive result is obtained. We prove an oracle inequality for the regretof the proposed estimator compared with the optimal Bayes risk,under some conditions.The oracle inequality leads to the property that the ratio of the proposed estimator tothat of the Bayes procedure approaches one, under mild conditins.Additionally, we demonstrate the performance of the estimator in simulation exper-iments with sparse and normal setups. It turns out that the proposed procedure indeedimproves over its kernel version in sparse and nonsparse setups.