高维数据空间的协方差矩阵迹的比率相合性  

The Ratio-Consistent Estimators of Covariance Matrices in High-Dimensional Data

作　　者：王理同 薛腾腾 唐林俊 WANG Li-tong;XUE Teng-tengi;TANG Lin-jun(Zhejiang University of Technology,Department of Applied Mathematics,Hangzhou 310032,China;Jiaxing University,Department of Statistics,Jiaxing 314001,China)

机构地区：[1]浙江工业大学应用数学系,浙江杭州310032 [2]嘉兴学院统计系,湖南嘉兴314001

出　　处：《数学的实践与认识》2018年第19期242-245,共4页Mathematics in Practice and Theory

基　　金：浙江省自然科学基金项目(LY16A010019,LY16A010021,LY15A010019)

摘　　要：在处理高维数据的检验和分类等问题时，涉及到协方差矩阵的估计．而在高维数据领域，协方差矩阵估计的精度将对诸如检验和分类等问题起到非常重要的影响．主要考虑多样本条件下协方差矩阵的比率相合性问题，证明了两样本和三样本情况下的高维数据协方差矩阵比率相合性．It is necessary to estimate the covariance matrix when we process hypothesis and classification problems in the high-dimensional data. While in high dimensional data field, the estimation accuracy will play a very important influence. This paper is mainly concerned with the ratio-consistent estimators of covariance matrices in high-dimensional data. Several theorems involved the ratio-consistent estimators of covariance matrices are proved under two samples and three samples in high dimension data.

关 键 词：比率相合性 高维数据 协方差矩阵估计 

分 类 号：O212.1[理学—概率论与数理统计]