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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. Ahmad, Rauf, 2022. "Tests for proportionality of matrices with large dimension," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. Xu, Kai & Tian, Yan & He, Daojiang, 2021. "A high dimensional nonparametric test for proportional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    3. 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).

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