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

Koji Tsukuda, Shun Matsuura

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number104822
JournalJournal of Multivariate Analysis
Volume186
DOIs
Publication statusPublished - Nov 2021

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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