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High-dimensional testing for proportional covariance matrices

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  • Tsukuda, Koji
  • Matsuura, Shun

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≍pδ 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.

Suggested Citation

  • Tsukuda, Koji & Matsuura, Shun, 2019. "High-dimensional testing for proportional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 412-420.
    • Handle: RePEc:eee:jmvana:v:171:y:2019:i:c:p:412-420
    DOI: 10.1016/j.jmva.2019.01.011
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    References listed on IDEAS

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    Cited by:

    1. Xu, Kai & Tian, Yan & He, Daojiang, 2021. "A high dimensional nonparametric test for proportional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    2. Tsukuda, Koji & Matsuura, Shun, 2021. "Limit theorem associated with Wishart matrices with application to hypothesis testing for common principal components," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    3. Ahmad, Rauf, 2022. "Tests for proportionality of matrices with large dimension," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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