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Infinitely divisible matrix gamma distribution: Asymptotic behaviour and parameters estimation

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  • Masmoudi, Afif
  • Rejeb, Hajer

Abstract

In this research paper, we investigate an infinitely divisible p×p matrix gamma distribution AΓp(η,Σ), with parameters η>(p−1)/2 and Σ, concentrated on the cone of symmetric positive definite matrices. The parameter Σ is supposed to be a symmetric positive definite p×p matrix. We also display some of its fundamental properties. Additionally, we identify the link between this multivariate gamma distribution and the Wishart one, which leads us to prove that AΓp(η,Σ) distribution is asymptotically a stochastic linear combination of Wishart matrices. Moreover, we provide an explicit expression of the parameters estimators using the method of moments. Eventually, we exhibit a new simulation algorithm, grounded on the obtained results, in order to illustrate the performance of these estimators.

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  • Masmoudi, Afif & Rejeb, Hajer, 2023. "Infinitely divisible matrix gamma distribution: Asymptotic behaviour and parameters estimation," Statistics & Probability Letters, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:stapro:v:194:y:2023:i:c:s016771522200270x
    DOI: 10.1016/j.spl.2022.109757
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    References listed on IDEAS

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    1. Pérez-Abreu, Victor & Stelzer, Robert, 2014. "Infinitely divisible multivariate and matrix Gamma distributions," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 155-175.
    2. Bodnar, Taras & Okhrin, Yarema, 2008. "Properties of the singular, inverse and generalized inverse partitioned Wishart distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2389-2405, November.
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