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From moments of sum to moments of product

  • Kan, Raymond
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    We provide an identity that relates the moment of a product of random variables to the moments of different linear combinations of the random variables. Applying this identity, we obtain new formulae for the expectation of the product of normally distributed random variables and the product of quadratic forms in normally distributed random variables. In addition, we generalize the formulae to the case of multivariate elliptically distributed random variables. Unlike existing formulae in the literature, our new formulae are extremely efficient for computational purposes.

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    File URL: http://www.sciencedirect.com/science/article/B6WK9-4N0X5M7-1/2/dc61319752f2b348deaaab59d8d12b5c
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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 99 (2008)
    Issue (Month): 3 (March)
    Pages: 542-554

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    Handle: RePEc:eee:jmvana:v:99:y:2008:i:3:p:542-554
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    1. Blacher, René, 2003. "Multivariate quadratic forms of random vectors," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 2-23, October.
    2. Schott, James R., 2003. "Kronecker product permutation matrices and their application to moment matrices of the normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 177-190, October.
    3. repec:ner:tilbur:urn:nbn:nl:ui:12-153208 is not listed on IDEAS
    4. repec:ner:tilbur:urn:nbn:nl:ui:12-153219 is not listed on IDEAS
    5. Berkane, Maia & Bentler, P. M., 1986. "Moments of elliptically distributed random variates," Statistics & Probability Letters, Elsevier, vol. 4(6), pages 333-335, October.
    6. repec:ner:tilbur:urn:nbn:nl:ui:12-153205 is not listed on IDEAS
    7. Magnus, J.R., 1986. "The exact moments of a ratio of quadratic forms in normal variables," Other publications TiSEM c6725407-ac3c-44fd-b6d1-5, Tilburg University, School of Economics and Management.
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