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Testing block-diagonal covariance structure for high-dimensional data under non-normality

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  • Yamada, Yuki
  • Hyodo, Masashi
  • Nishiyama, Takahiro

Abstract

In this article, we propose a test for making an inference about the block-diagonal covariance structure of a covariance matrix in non-normal high-dimensional data. We prove that the limiting null distribution of the proposed test is normal under mild conditions when its dimension is substantially larger than its sample size. We further study the local power of the proposed test. Finally, we study the finite-sample performance of the proposed test via Monte Carlo simulations. We demonstrate the relevance and benefits of the proposed approach for a number of alternative covariance structures.

Suggested Citation

  • Yamada, Yuki & Hyodo, Masashi & Nishiyama, Takahiro, 2017. "Testing block-diagonal covariance structure for high-dimensional data under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 305-316.
    • Handle: RePEc:eee:jmvana:v:155:y:2017:i:c:p:305-316
    DOI: 10.1016/j.jmva.2016.12.009
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    References listed on IDEAS

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    Cited by:

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    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. Ivair R. Silva & Yan Zhuang & Julio C. A. da Silva Junior, 2022. "Kronecker delta method for testing independence between two vectors in high-dimension," Statistical Papers, Springer, vol. 63(2), pages 343-365, April.
    4. Dörnemann, Nina, 2023. "Likelihood ratio tests under model misspecification in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    5. Bodnar, Taras & Dette, Holger & Parolya, Nestor, 2019. "Testing for independence of large dimensional vectors," MPRA Paper 97997, University Library of Munich, Germany, revised May 2019.
    6. Dette, Holger & Dörnemann, Nina, 2020. "Likelihood ratio tests for many groups in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 178(C).

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