The Compound Estimation Of Normal Means And Possion Means

This paper mainly studies the compound estimation of normal means and Possion means.For the compound estimation of normal means, we establish the relationship with the Bayes estimation of a single normal mean, then it can be transformed into a univariate normal mean estimation problem, but for this problem,the prior distribution is not known,so we propose a general maximum likelihood empirical Bayes(GMLEB),through the EM algorithm and convex optimization methods solving this estimation;For the compound estimation of Possion means,first we gives the empirical Bayes estimation by Robbins,but this estimation is not monotonic and the convergence speed is very slow,so it is necessary to improve the empirical Bayes estimation,thereby we review the three-step improvement for the classical Possion empirical Bayes estimation,and at the same time,we also give the Possion GMLEB estimation and the GMLEB estimation after transforming Possion to normality approximately.In order to compare the e?ect of this several estimation methods, we give some simulation at the end of this paper,it shows that the three-step improvement and two GMLEB estimation have a significant reduce than the empirical Bayes estimation in mean square error,and the estimated e?ect has an obvious promotion.