Bartlett分解与多元正态总体均值的广义推断  

Bartlett's Decomposition and Generalized Inferences on the Means of Several Multivariate Normal Populations

作　　者：范永辉[1] 王松桂[2] 

机构地区：[1]河北师范大学数学与信息科学学院,石家庄050016 [2]北京工业大学应用数理学院,北京100022

出　　处：《数学学报（中文版）》2010年第2期329-340,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10926071);河北师范大学博士基金支持项目(130142)

摘　　要：对多个正态总体均值的统计推断是一个古老而令人感兴趣的问题.本文利用样本协方差矩阵的Bartlett分解和广义p-值的概念给出一些关于均值的精确检验.模拟显示这些检验比已有的检验有更高的功效.同时,还根据协方差矩阵的Bartlett分解和样本均值向量,得到一个分布和未知参数无关的统计量,用它可以对多个正态总体共同均值做精确检验.模拟显示,这些检验犯第一错误的概率小于显著性水平,而且有更高的检验功效.Inference on the mean vectors of several multivariate normal populations is an old and interesting problem. In this paper, by the distribution of the Bartlett＇s decomposition of sample covariance matrices, the concepts of an exact tests are proposed. Simulation shows these tests are more powerful than the existing tests. Also, by the Bartlett＇s decomposition of sample covariance matrices and the sample mean vectors, two generalized tests and a new traditional test are proposed to test the common mean of several multivariate normal populations. Simulation shows that the type I error probability of these tests is less than the nominal level and has more powers.

关 键 词：广义P-值 广义置信域 Behrens—Fisher问题 

分 类 号：O212.4[理学—概率论与数理统计]