Likelihood ratio test for covariance matrix under multivariate t distribution with uncorrelated observations

Katarzyna Filipiak, Daniel Klein, Stepan Mazur and Malwina Mrowińska

Journal of Multivariate Analysis, 2025, vol. 210, issue C

Abstract: In this paper, estimators for the unknown parameters under two types of matrix-variate t distributions are determined, and their basic statistical properties, including bias and sufficiency, are investigated. These estimators are then applied to test hypotheses concerning the covariance structure of a multivariate t distribution associated with a collection of uncorrelated, though not necessarily independent, observation vectors, using two types of matrix-variate t distributions. A likelihood ratio test is proposed, and its distributional properties under the null hypothesis are examined, assuming either a fully specified covariance matrix or one specified up to a constant. Furthermore, it is demonstrated that the asymptotic distribution for the type I matrix-variate t distribution under both hypotheses coincides with that under the normality assumption. Finally, for testing a fully specified covariance matrix, the asymptotic distribution of the likelihood ratio test statistic is determined.

Keywords: Covariance structure; Likelihood ratio test; Matrix-variate t distribution; Maximum likelihood estimators; Multivariate t distribution (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.jmva.2025.105490

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