基于随机矩阵理论的高维数据球形检验  

Sphericity Test for High Dimensional Data Based on Random Matrix Theory

作　　者：袁守成 周杰[1] 沈洁琼 YUAN Shoucheng;ZHOU Jie;SHEN Jieqiong(College of Mathematics,Sichuan University,Chendu,610064,China;College of Mathematics and Statistical Science,Puer University,Puer,665000,China;School of Computer and Data Engineering,Zhejiang University Ningbo Institute of Technology,Ningbo,315100,China)

机构地区：[1]四川大学数学学院,成都610064 [2]普洱学院数学与统计学院,普洱665000 [3]浙江大学宁波理工学院计算机与数据工程学院,宁波315100

出　　处：《应用概率统计》2020年第4期355-364,共10页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:61374027、11871357);云南省教育厅科学研究基金项目(批准号:2018JS516)资助。

摘　　要：本文基于随机矩阵理论,研究了一般总体的高维协方差矩阵的球形检验.当样本量小于数据维数时,经典的似然比检验方法在球形检验中已无法使用.通过引入样本协方差矩阵谱分布的高阶矩,构造出一个新的检验统计量,并给出其在零假设下的渐近分布.模拟实验表明所提出的统计量在控制第一类错误概率的基础上能有效提高检验功效,对于Spiked模型效果尤为显著.In this article we study test of sphericity for high-dimensional covariance matrix in the general population based on random matrix theory.When the sample size is less than data dimension,the classical likelihood ratio test has poor performance for test of sphericity.Thus,we propose a new statistic for test of sphericity by using the higher moments of spectral distribution of the sample covariance matrix,and derive the asymptotic distribution of the statistic under the null hypothesis.Simulation results show that the proposed statistics can e ectively improve the power of the test of sphericity for high dimensional data,and have especially signi cant e ects for Spiked model,on the basis of controlling the type-one error probability.

关 键 词：高维协方差矩阵 球形检验 谱分布 检验功效 

分 类 号：O212.1[理学—概率论与数理统计]