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

Katarzyna Filipiak (), Mateusz John () and Yuli Liang
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Katarzyna Filipiak: Poznań University of Technology
Mateusz John: Poznań University of Technology

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2024, vol. 33, issue 3, No 13, 847-876

Abstract: 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.

Keywords: Doubly multivariate model; Covariance structure; Quadratic subspace; Rao score test; Likelihood ratio test; 62H15; 62E20; 62E15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11749-024-00922-0

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