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Discrepancy between structured matrices in the power analysis of a separability test

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  • Filipiak, Katarzyna
  • Klein, Daniel
  • Mokrzycka, Monika

Abstract

An important task in the analysis of multivariate data is testing of the covariance matrix structure. In particular, for assessing separability, various tests have been proposed. However, the development of a method of measuring discrepancy between two covariance matrix structures, in relation to the study of the power of the test, remains an open problem. Therefore, a discrepancy measure is proposed such that for two arbitrary alternative hypotheses with the same value of discrepancy, the power of tests remains stable, while for increasing discrepancy the power increases. The basic hypothesis is related to the separable structure of the observation matrix under a doubly multivariate normal model, as assessed by the likelihood ratio and Rao score tests. It is shown that the particular one-parameter method and the Frobenius norm fail in the power analysis of tests, while the entropy and quadratic loss functions can be efficiently used to measure the discrepancy between separable and non-separable covariance structures for a multivariate normal distribution.

Suggested Citation

  • Filipiak, Katarzyna & Klein, Daniel & Mokrzycka, Monika, 2024. "Discrepancy between structured matrices in the power analysis of a separability test," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:csdana:v:192:y:2024:i:c:s0167947323002189
    DOI: 10.1016/j.csda.2023.107907
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    References listed on IDEAS

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    1. Soloveychik, I. & Trushin, D., 2016. "Gaussian and robust Kronecker product covariance estimation: Existence and uniqueness," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 92-113.
    2. Magnus, Jan R. & Neudecker, H., 1986. "Symmetry, 0-1 Matrices and Jacobians: A Review," Econometric Theory, Cambridge University Press, vol. 2(2), pages 157-190, August.
    3. 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.
    4. Emilie Devijver & Mélina Gallopin, 2018. "Block-Diagonal Covariance Selection for High-Dimensional Gaussian Graphical Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 306-314, January.
    5. Filipiak, Katarzyna & Klein, Daniel & Roy, Anuradha, 2016. "Score test for a separable covariance structure with the first component as compound symmetric correlation matrix," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 105-124.
    6. Mitchell, Matthew W. & Genton, Marc G. & Gumpertz, Marcia L., 2006. "A likelihood ratio test for separability of covariances," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1025-1043, May.
    7. Manceur, A.M. & Dutilleul, P., 2013. "Unbiased modified likelihood ratio tests for simple and double separability of a variance–covariance structure," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 631-636.
    8. Lu, Nelson & Zimmerman, Dale L., 2005. "The likelihood ratio test for a separable covariance matrix," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 449-457, July.
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