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

Koji Tsukuda, Shun Matsuura

研究成果: Article査読

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English
論文番号104822
ジャーナルJournal of Multivariate Analysis
186
DOI
出版ステータスPublished - 2021 11

ASJC Scopus subject areas

  • 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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