The Method Of Compound Estimation Of High-dimensional Mixture Normal Means And Its Application

This paper mainly studies the method of the compound estimation of High-dimensional mixture normal means and its application. In this paper, the problem of the compound estimation of normal means is transformed into the Bayes estimation of a single random mean. But the prior distribution G in the Bayes estimation is unknown. In order to solve this problem, the general maximum likelihood empirical Bayes method proposed by Jiang and Zhang [21] is introduced. In other words, we firstly estimate the empirical distribution of the unknown means by the generalized maximum likelihood estimator(MLE) and then plug the estimator into the oracle gen-eral EB rule.In the problem of sparse normal means testing, we use GMLEB method in this paper to estimate the prior distribution of normal mean/xand then use the likelihood ratio test, this method is called the generalized likelihood ratio test (GLRT). In ad-dition, this paper also introduces the method of the other two multiple comparison method HC test and BJ test, finally we has carried on some simulations, the results show that GLRT is a very competitive test method.