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The Matsumoto–Yor property on trees for matrix variates of different dimensions

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  • Bobecka, Konstancja

Abstract

The paper is devoted to an extension of the multivariate Matsumoto–Yor (MY) independence property with respect to a tree with p vertices to the case where random variables corresponding to the vertices of the tree are replaced by random matrices. The converse of the p-variate MY property, which characterizes the product of one gamma and p−1 generalized inverse Gaussian distributions, is extended to characterize the product of the Wishart and p−1 matrix generalized inverse Gaussian distributions.

Suggested Citation

  • Bobecka, Konstancja, 2015. "The Matsumoto–Yor property on trees for matrix variates of different dimensions," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 22-34.
    • Handle: RePEc:eee:jmvana:v:141:y:2015:i:c:p:22-34
    DOI: 10.1016/j.jmva.2015.05.018
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    References listed on IDEAS

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    1. Koudou, Angelo Efoévi, 2006. "A link between the Matsumoto-Yor property and an independence property on trees," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1097-1101, June.
    2. Koudou, Angelo Efoevi, 2012. "A Matsumoto–Yor property for Kummer and Wishart random matrices," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1903-1907.
    3. V. Seshadri & J. Wesołowski, 2008. "More on connections between Wishart and matrix GIG distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(2), pages 219-232, September.
    4. Ronald W. Butler, 1998. "Generalized Inverse Gaussian Distributions and their Wishart Connections," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 69-75, March.
    5. Massam, Hélène & Wesolowski, Jacek, 2006. "The Matsumoto-Yor property and the structure of the Wishart distribution," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 103-123, January.
    6. Matsumoto, Hiroyuki & Yor, Marc, 2003. "Interpretation via Brownian motion of some independence properties between GIG and gamma variables," Statistics & Probability Letters, Elsevier, vol. 61(3), pages 253-259, February.
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    Cited by:

    1. Piliszek, Agnieszka & Wesołowski, Jacek, 2016. "Kummer and gamma laws through independences on trees—Another parallel with the Matsumoto–Yor property," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 15-27.
    2. Wesołowski, Jacek, 2015. "On the Matsumoto–Yor type regression characterization of the gamma and Kummer distributions," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 145-149.
    3. Bartosz Kołodziejek, 2017. "The Matsumoto–Yor Property and Its Converse on Symmetric Cones," Journal of Theoretical Probability, Springer, vol. 30(2), pages 624-638, June.
    4. Letac, Gérard & Wesołowski, Jacek, 2020. "Multivariate reciprocal inverse Gaussian distributions from the Sabot–Tarrès–Zeng integral," Journal of Multivariate Analysis, Elsevier, vol. 175(C).

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