Sphericity and Identity Test for High-dimensional Covariance Matrix Using Random Matrix Theory  

作　　者：Shou-cheng YUAN Jie ZHOU Jian-xin PAN Jie-qiong SHEN 

机构地区：[1]College of Mathematics,Sichuan University,Chengdu 610064,China [2]School of Mathematics,University of Manchester,Manchester M139PL,UK [3]School of Computer and Data Engineering,Zhejiang University Ningbo Institute of Technology,Ningbo 315100,China

出　　处：《Acta Mathematicae Applicatae Sinica》2021年第2期214-231,共18页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.61374027,11871357);the Sichuan Science and Technology Program(Nos.2019YJ0122)。

摘　　要：This paper addresses the issue of testing sphericity and identity of high-dimensional population covariance matrix when the data dimension exceeds the sample size.The central limit theorem of the first four moments of eigenvalues of sample covariance matrix is derived using random matrix theory for generally distributed populations.Further,some desirable asymptotic properties of the proposed test statistics are provided under the null hypothesis as data dimension and sample size both tend to infinity.Simulations show that the proposed tests have a greater power than existing methods for the spiked covariance model.

关 键 词：sphericity test identity test high-dimensional covariance matrix spiked model spectral distribution 

分 类 号：O212[理学—概率论与数理统计]