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Testing independence under a block compound symmetry covariance structure

Author

Listed:
  • Katarzyna Filipiak

    (Poznań University of Technology)

  • Mateusz John

    (Poznań University of Technology)

  • Daniel Klein

    (P. J. Šafárik University)

Abstract

The goal of this article is to test the hypothesis related to the independence of features between any two repeated measures in a block compound symmetry structure under the doubly multivariate normal model. The Rao score and Wald test statistics are determined and the characteristic function of the likelihood ratio test statistic is presented. For all of these test statistics, the asymptotic distributional properties are compared using simulation studies, and the robustness of the empirical distributions is considered. Furthermore, for power analysis purpose, the Kullback-Leibler divergence is proposed to measure discrepancy between hypotheses and the power of each mentioned tests, as well as F-test and Roy’s largest root test, is studied. Finally, all mentioned tests are applied to a real data example.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:2:d:10.1007_s00362-022-01335-7
    DOI: 10.1007/s00362-022-01335-7
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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. Roy, Anuradha & Leiva, Ricardo & Žežula, Ivan & Klein, Daniel, 2015. "Testing the equality of mean vectors for paired doubly multivariate observations in blocked compound symmetric covariance matrix setup," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 50-60.
    3. Leiva, Ricardo, 2007. "Linear discrimination with equicorrelated training vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 384-409, February.
    4. Roy, Anuradha & Zmyślony, Roman & Fonseca, Miguel & Leiva, Ricardo, 2016. "Optimal estimation for doubly multivariate data in blocked compound symmetric covariance structure," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 81-90.
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    Cited by:

    1. Katarzyna Filipiak & Tõnu Kollo, 2024. "Covariance structure tests for multivariate t-distribution," Statistical Papers, Springer, vol. 65(7), pages 4537-4566, September.

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