TY - JOUR
T1 - Limit theorem associated with Wishart matrices with application to hypothesis testing for common principal components
AU - Tsukuda, Koji
AU - Matsuura, Shun
N1 - Funding Information:
The authors would like to express their gratitude to the associate editor and the referees who provided valuable comments. The authors also would like to thank the editor who provided many suggestions for improving the presentation and shortening the paper. This study was supported in part by Japan Society for the Promotion of Science KAKENHI Grant Numbers 18K13454 , 20K11713 , and 21K13836 . This study was partly carried out when the first author was a member of Graduate School of Arts and Sciences, the University of Tokyo.
Funding Information:
The authors would like to express their gratitude to the associate editor and the referees who provided valuable comments. The authors also would like to thank the editor who provided many suggestions for improving the presentation and shortening the paper. This study was supported in part by Japan Society for the Promotion of Science KAKENHI Grant Numbers 18K13454, 20K11713, and 21K13836. This study was partly carried out when the first author was a member of Graduate School of Arts and Sciences, the University of Tokyo.
Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2021/11
Y1 - 2021/11
N2 - This paper describes the derivation of a new property of the Wishart distribution when the degrees of freedom and the sizes of scale matrices grow simultaneously. In particular, the asymptotic normality of the trace of the product of four independent Wishart matrices is demonstrated for a high-dimensional asymptotic regime. As an application of the result, a statistical test procedure for the common principal components hypothesis is proposed. For this problem, the proposed test statistic is asymptotically normal under the null hypothesis and diverges to positive infinity in probability under the alternative hypothesis.
AB - This paper describes the derivation of a new property of the Wishart distribution when the degrees of freedom and the sizes of scale matrices grow simultaneously. In particular, the asymptotic normality of the trace of the product of four independent Wishart matrices is demonstrated for a high-dimensional asymptotic regime. As an application of the result, a statistical test procedure for the common principal components hypothesis is proposed. For this problem, the proposed test statistic is asymptotically normal under the null hypothesis and diverges to positive infinity in probability under the alternative hypothesis.
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U2 - 10.1016/j.jmva.2021.104822
DO - 10.1016/j.jmva.2021.104822
M3 - Article
AN - SCOPUS:85115011945
SN - 0047-259X
VL - 186
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
M1 - 104822
ER -