双样本协方差矩阵和均值向量齐性检验的研究及其应用

A Study on the Testing of Equal Mean & Covariance Matrix and Its Application

物证检验问题可以转化为双样本均值向量的检验和协方差矩阵的检验之统计理论问题 .对于检验统计量 T2、λ3,虽然 Hotelling对均值向量的检验给出了具有许多优良性质的 T2统计量 ,但它使用的前提条件是现场和嫌疑人的样本量必须同时大于特征数 ,这在物证检验中很难满足 ,本文的拓宽了使用条件 ,使其在物证检验中能够广泛使用 ;本文采用了统计模拟的方法构造了检验均值向量和协方差阵同时相等的统计量λ4 的上 1 0 0α%分位数表 ,这就为物证检验提供了新工具 ,将对于揭露和打击犯罪、保障国家的安全与社会的稳定具有重大的社会效益 .最后给出了应用实例 .

The evidence test with quantitative characteristic can concert to the problem of statistics theories with two-sample average vecdtor and covariance matrix testing at the same time. However,no one can provide about λ_4 distribution and application. This thesis uses the mehtod of statistical simulation to give us the experience distribution, and then work out the λ_4 upper 100α quantile table and its error talbe,apply it to the evidence test. Finally,this thesis provides one practical cases.