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Testing covariance structures belonging to a quadratic subspace under a doubly multivariate model

Author

Listed:
  • Katarzyna Filipiak

    (Poznań University of Technology)

  • Mateusz John

    (Poznań University of Technology)

  • Yuli Liang

    (Linnaeus University)

Abstract

A hypothesis related to the block structure of a covariance matrix under the doubly multivariate normal model is studied. It is assumed that the block structure of the covariance matrix belongs to a quadratic subspace, and under the null hypothesis, each block of the covariance matrix also has a structure belonging to some quadratic subspace. The Rao score and the likelihood ratio test statistics are derived, and the exact distribution of the likelihood ratio test is determined. Simulation studies show the advantage of the Rao score test over the likelihood ratio test in terms of speed of convergence to the limiting chi-square distribution, while both proposed tests are competitive in terms of their power. The results are applied to both simulated and real-life example data.

Suggested Citation

  • Katarzyna Filipiak & Mateusz John & Yuli Liang, 2024. "Testing covariance structures belonging to a quadratic subspace under a doubly multivariate model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(3), pages 847-876, September.
    • Handle: RePEc:spr:testjl:v:33:y:2024:i:3:d:10.1007_s11749-024-00922-0
    DOI: 10.1007/s11749-024-00922-0
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    References listed on IDEAS

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    1. Yuli Liang & Dietrich Rosen & Tatjana Rosen, 2015. "On estimation in hierarchical models with block circular covariance structures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 773-791, August.
    2. Lin, Lijing & Higham, Nicholas J. & Pan, Jianxin, 2014. "Covariance structure regularization via entropy loss function," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 315-327.
    3. Klein, Daniel & Pielaszkiewicz, Jolanta & Filipiak, Katarzyna, 2022. "Approximate normality in testing an exchangeable covariance structure under large- and high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    4. Kato, Naohiro & Yamada, Takayuki & Fujikoshi, Yasunori, 2010. "High-dimensional asymptotic expansion of LR statistic for testing intraclass correlation structure and its error bound," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 101-112, January.
    5. Linqi Yi & Junshan Xie, 2018. "A high-dimensional likelihood ratio test for circular symmetric covariance structure," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(6), pages 1392-1402, March.
    6. Katarzyna Filipiak & Mateusz John & Daniel Klein, 2023. "Testing independence under a block compound symmetry covariance structure," Statistical Papers, Springer, vol. 64(2), pages 677-704, April.
    Full references (including those not matched with items on IDEAS)

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