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On the structure of the Wishart distribution

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  • Shanbhag, D. N.
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    Abstract

    In this paper it is shown that every nonnegative definite symmetric random matrix with independent diagonal elements and at least one nondegenerate nondiagonal element has a noninfinitely divisible distribution. Using this result it is established that every Wishart distribution Wp(k, [Sigma], M) with both p and rank ([Sigma]) >= 2 is noninfinitely divisible. The paper also establishes that any Wishart matrix having distribution Wp(k, [Sigma], 0) has the joint distribution of its elements in the rth row and rth column to be infinitely divisible for every r = 1,2,...,p.

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    Bibliographic Info

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

    Volume (Year): 6 (1976)
    Issue (Month): 3 (September)
    Pages: 347-355

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    Handle: RePEc:eee:jmvana:v:6:y:1976:i:3:p:347-355

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    Related research

    Keywords: Wishart distribution infinitely divisible distributions;

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    Cited by:
    1. Sapatinas, Theofanis & Shanbhag, Damodar N., 2010. "Moment properties of multivariate infinitely divisible laws and criteria for multivariate self-decomposability," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 500-511, March.

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