High-dimensional proportionality test of two covariance matrices and its application to gene expression data  

作　　者：Long Feng Xiaoxu Zhang Binghui Liu 

机构地区：[1]School of Statistics and Data Science,LPMC and KLMDASR,Nankai University,Tianjin,People’s Republic of China [2]School of Mathematics and Statistics and KLAS,Northeast Normal University,Changchun,People’s Republic of China

出　　处：《Statistical Theory and Related Fields》2022年第2期161-174,共14页统计理论及其应用（英文）

基　　金：This work was supported by the National Natural Sci-ence Foundation of China[Grant Numbers 11501092,11571068];the Special Fund for Key Laboratories of Jilin Province,China[Grant Number 20190201285JC].

摘　　要：With the development of modern science and technology, more and more high-dimensionaldata appear in the application fields. Since the high dimension can potentially increase the com-plexity of the covariance structure, comparing the covariance matrices among populations isstrongly motivated in high-dimensional data analysis. In this article, we consider the proportion-ality test of two high-dimensional covariance matrices, where the data dimension is potentiallymuch larger than the sample sizes, or even larger than the squares of the sample sizes. We devisea novel high-dimensional spatial rank test that has much-improved power than many exist-ing popular tests, especially for the data generated from some heavy-tailed distributions. Theasymptotic normality of the proposed test statistics is established under the family of ellipticallysymmetric distributions, which is a more general distribution family than the normal distribu-tion family, including numerous commonly used heavy-tailed distributions. Extensive numericalexperiments demonstrate the superiority of the proposed test in terms of both empirical sizeand power. Then, a real data analysis demonstrates the practicability of the proposed test forhigh-dimensional gene expression data.

关 键 词：Covariance matrices elliptically symmetric distributions high dimension test PROPORTIONALITY spatial rank 

分 类 号：O15[理学—数学]