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

Koji Tsukuda, Shun Matsuura

## 抄録

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.

本文言語 英語 104822 Journal of Multivariate Analysis 186 https://doi.org/10.1016/j.jmva.2021.104822 出版済み - 11 2021

## All Science Journal Classification (ASJC) codes

• 統計学および確率
• 数値解析
• 統計学、確率および不確実性

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