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Maximum likelihood estimation for singular Wishart distributions

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  • Asai, Manabu

Abstract

This paper utilizes the Bartlett decomposition of a singular Wishart variable to derive the log-expectation. A re-parameterization for maximum likelihood estimation is proposed to separately estimate the scale matrix and the degrees-of-freedom parameter. Its asymptotic and finite-sample properties are investigated.

Suggested Citation

  • Asai, Manabu, 2026. "Maximum likelihood estimation for singular Wishart distributions," Statistics & Probability Letters, Elsevier, vol. 229(C).
    • Handle: RePEc:eee:stapro:v:229:y:2026:i:c:s016771522500224x
    DOI: 10.1016/j.spl.2025.110579
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    References listed on IDEAS

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    1. Kubokawa, Tatsuya & Srivastava, Muni S., 2008. "Estimation of the precision matrix of a singular Wishart distribution and its application in high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1906-1928, October.
    2. Gustav Alfelt & Taras Bodnar & Farrukh Javed & Joanna Tyrcha, 2023. "Singular Conditional Autoregressive Wishart Model for Realized Covariance Matrices," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(3), pages 833-845, July.
    3. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
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