高维正态均值的混合估计方法及其应用

发布时间：2018-01-16 21:38

本文关键词：高维正态均值的混合估计方法及其应用　出处：《苏州大学》2015年硕士论文　论文类型：学位论文

【摘要】：本文主要研究了高维正态均值的混合估计方法以及该方法在多重比较问题中的应用。文中将高维正态均值的混合估计问题转化为单变量正态均值的估计问题,而在单变量正态均值的贝叶斯估计中,其先验分布G未知。为了有效地解决这个问题,文中介绍了由Jiang和Zhang提出的广义极大似然估计方法(GMLEB)[21]来估计G,也就是说,将贝叶斯估计中的先验分布换成它的极大似然估计。文中还介绍利用EM算法和凸优化方法来解决GMLEB的计算问题。在稀疏正态均值的检验问题中,文中利用GMLEB方法估计出正态均值μ的先验分布然后再用似然比检验,此方法称为广义似然比检验(GLRT)。此外,文中还介绍了其他两种多重比较的方法即HC检验和BJ检验,最后进行了数据实验模拟,结果表明GLRT是一种非常有竞争力的检验方法。
[Abstract]:In this paper, the mixed estimation method of high dimensional normal mean and its application in multiple comparison problems are studied. In this paper, the mixed estimation problem of high dimensional normal mean is transformed into the estimation of univariate normal mean. The prior distribution G is unknown in the Bayesian estimation of the normal mean of a single variable in order to solve this problem effectively. The generalized maximum likelihood estimation method proposed by Jiang and Zhang is introduced in this paper. [To estimate G, that is to say. The priori distribution in Bayesian estimation is replaced by its maximum likelihood estimator. EM algorithm and convex optimization method are also introduced to solve the GMLEB problem. In this paper, the prior distribution of normal mean 渭 is estimated by GMLEB method, and then the likelihood ratio test is used. This method is called generalized likelihood ratio test. Two other multi-comparison methods, HC test and BJ test, are also introduced in this paper. Finally, the data are simulated and the results show that GLRT is a very competitive test method.
【学位授予单位】：苏州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212

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