High-dimensional testing for proportional covariance matrices

Koji Tsukuda, Shun Matsuura

Research output: Contribution to journalArticle

Abstract

Hypothesis testing for the proportionality of covariance matrices is a classical statistical problem and has been widely studied in the literature. However, there have been few treatments of this test in high-dimensional settings, especially for the case where the number of variables is larger than the sample size, despite high-dimensional statistical inference having recently received considerable attention. This paper studies hypothesis testing for the proportionality of two covariance matrices in the high-dimensional setting: m,n≍p δ for some δ∈(1∕2,1), where m and n denote the sample sizes and p denotes the number of variables. A test statistic is proposed and its asymptotic distribution is derived under multivariate normality. The non-asymptotic performance of the proposed test procedure is numerically examined.

Original languageEnglish
Pages (from-to)412-420
Number of pages9
JournalJournal of Multivariate Analysis
Volume171
DOIs
Publication statusPublished - 2019 May 1

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Keywords

  • Asymptotic test
  • High-dimension
  • Multivariate normal distribution
  • Proportional covariance model

ASJC Scopus subject areas

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

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