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

Author

Listed:
  • Filipiak, Katarzyna
  • Klein, Daniel
  • Mazur, Stepan
  • Mrowińska, Malwina

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.

Suggested Citation

  • Filipiak, Katarzyna & Klein, Daniel & Mazur, Stepan & Mrowińska, Malwina, 2025. "Likelihood ratio test for covariance matrix under multivariate t distribution with uncorrelated observations," Journal of Multivariate Analysis, Elsevier, vol. 210(C).
    • Handle: RePEc:eee:jmvana:v:210:y:2025:i:c:s0047259x25000855
    DOI: 10.1016/j.jmva.2025.105490
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    References listed on IDEAS

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    1. Katarzyna Filipiak & Tõnu Kollo, 2024. "Covariance structure tests for multivariate t-distribution," Statistical Papers, Springer, vol. 65(7), pages 4537-4566, September.
    2. Arjun K. Gupta & Tamas Varga & Taras Bodnar, 2013. "Elliptically Contoured Models in Statistics and Portfolio Theory," Springer Books, Springer, edition 2, number 978-1-4614-8154-6, January.
    3. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549, Enero-Abr.
    4. Karlsson, Sune & Mazur, Stepan & Nguyen, Hoang, 2023. "Vector autoregression models with skewness and heavy tails," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    5. Kiss, Tamás & Mazur, Stepan & Nguyen, Hoang, 2022. "Predicting returns and dividend growth — The role of non-Gaussian innovations," Finance Research Letters, Elsevier, vol. 46(PA).
    6. Tamás Kiss & Stepan Mazur & Hoang Nguyen & Pär Österholm, 2023. "Modeling the relation between the US real economy and the corporate bond‐yield spread in Bayesian VARs with non‐Gaussian innovations," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(2), pages 347-368, March.
    7. Sutradhar, Brajendra C. & Ali, Mir M., 1989. "A generalization of the Wishart distribution for the elliptical model and its moments for the multivariate t model," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 155-162, April.
    8. Arjun K. Gupta & Daya K. Nagar, 2000. "Matrix-variate beta distribution," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 24, pages 1-11, January.
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    1. Daniela I. Flores-Silva & Miguel A. Sordo & Alfonso Su'arez-Llorens, 2025. "Probability equivalent level for CoVaR and VaR in bivariate Student-\textit{t} copulas with application to foreign exchange risk monitoring," Papers 2510.15934, arXiv.org.

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