Hypothesis testing for the identity of high-dimensional covariance matrices

A new test statistic is proposed by utilizing the eigenvalues of the sample covariance matrix for the identity test. Under some general assumptions, asymptotic distributions of the proposed test statistic T and tests proposed in previous literature (denoted as Ts,T1,T2) are given. Simulations are al...

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Bibliographic Details
Published in:Statistics & probability letters 2020-06, Vol.161, p.108699, Article 108699
Main Authors: Qian, Manling, Tao, Li, Li, Erqian, Tian, Maozai
Format: Article
Language:English
Subjects:
Covariance matrix
High-dimensional data
Hypothesis testing
Identity matrix
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Summary:A new test statistic is proposed by utilizing the eigenvalues of the sample covariance matrix for the identity test. Under some general assumptions, asymptotic distributions of the proposed test statistic T and tests proposed in previous literature (denoted as Ts,T1,T2) are given. Simulations are also conducted to evaluate their performance in a finite sample.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2020.108699