高维数据下两个正态总体均值的逐段检验  

A piecewise test of mean vector of two normal populations in high dimensional date

作　　者：苏荣娟 范永辉[1] SU Rong-juan;FAN Yong-hui(School of Mathematical Science,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《哈尔滨商业大学学报（自然科学版）》2023年第1期102-109,共8页Journal of Harbin University of Commerce：Natural Sciences Edition

摘　　要：高维数据下的均值检验是统计学检验的重要组成部分.在高维情形下,样本协方差矩阵往往是奇异矩阵,传统的均值检验方法因此失效.为解决该问题,对高维数据进行分段,使分得的每一段的维数均小于样本容量,继而运用Hotelling T 2检验依次对每一段进行检验,同时给出一种控制犯第一类错误的概率的新方法,使原假设下的检验水平稳定在事先给定的显著性水平左右.经模拟显示,该逐段检验方法比已有方法能更好地控制犯第一类错误的概率.Mean test of high dimensional data was an important part of test in statistics.In the high-dimensional state,the sample covariance matrix was often singular,so the traditional mean test method was invalid.In order to solve this problem,the high-dimensional data was segmented so that the dimension of each segment was smaller than the sample size,and then the Hotelling T 2 test was used to test each segment in turn.At the same time,a new method to control the probability of making the first type of errors was given,so that the test level under the original hypothesis was stable at the significance level given in advance.The simulation showed that the piecewise test method could control the probability of making the first type of errors betterthan the existing methods.

关 键 词：高维数据 均值检验 逐段检验 Hotelling T 2检验 检验水平 显著性水平 

分 类 号：O212.4[理学—概率论与数理统计]