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A note about measures and Jacobians of singular random matrices

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  • Díaz-García, José A.
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    Abstract

    This paper explains the differences between the densities and the Jacobians of the transforms of the same singular random matrices treated by several authors. Some comments on the results proposed by Srivastava [Singular Wishart and multivariate beta distributions, Ann. Statist. 31 (2003) 1537-1560] are presented. Definitions about a measure with respect to which a singular random matrix possesses a density are proposed. Finally two Jacobians of certain transforms under any of those measures are found.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 5 (May)
    Pages: 960-969

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:5:p:960-969

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    Keywords: Singular random matrices Jacobian of transformation Hausdorff measure Lebesgue measure Matrix-variate normal singular distribution;

    References

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    1. Díaz-García, José A. & González-Farías, Graciela, 2005. "Singular random matrix decompositions: distributions," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 109-122, May.
    2. Díaz-García, José A. & Jáimez, Ramón Gutierrez & Mardia, Kanti V., 1997. "Wishart and Pseudo-Wishart Distributions and Some Applications to Shape Theory," Journal of Multivariate Analysis, Elsevier, vol. 63(1), pages 73-87, October.
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    Cited by:
    1. Liu, Jin Shan & Ip, Wai Cheung & Wong, Heung, 2009. "Predictive inference for singular multivariate elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1440-1446, August.

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