Limit theorem associated with Wishart matrices with application to hypothesis testing for common principal components

[摘要] 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. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-11-01

[关键词] Asymptotic test;Central limit theorem;Common principal components model;High-dimension;Wishart distribution