| Bartlett分解与多元正态总体均值的广义推断 |
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| 引用本文： | 范永辉,王松桂. Bartlett分解与多元正态总体均值的广义推断[J]. 数学学报, 2010, 53(2): 329-340 |
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| 作者姓名： | 范永辉 王松桂 |
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| 作者单位： | 河北师范大学数学与信息科学学院;北京工业大学应用数理学院; |
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| 基金项目： | 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) |
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| 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.
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| 关 键 词： | 广义p-值 广义置信域 Behrens-Fisher问题 |
| 收稿时间： | 2007-02-15 |
| 修稿时间： | 2009-10-27 |
Bartlett's Decomposition and Generalized Inferences on the Means of Several Multivariate Normal Populations |
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| Yong Hui FAN College of Mathematics , Information Science,Hebei Normal University,Shijiazhuang ,P.R.China Song Gui WANG College of Applied Science,Beijing University of Technology,Beijing ,P.R.China. Bartlett's Decomposition and Generalized Inferences on the Means of Several Multivariate Normal Populations[J]. Acta Mathematica Sinica, 2010, 53(2): 329-340 |
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| Authors: | Yong Hui FAN College of Mathematics Information Science Hebei Normal University Shijiazhuang P.R.China Song Gui WANG College of Applied Science Beijing University of Technology Beijing P.R.China |
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| Affiliation: | 1. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, P. R. China;
2. College of Applied Science, Beijing University of Technology, Beijing 100022, P. R. China |
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| Abstract: | 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 ... |
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| Keywords: | generalized p value generalized confidence region Behrens Fisher problem |
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