From moments of sum to moments of product
AbstractWe 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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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 99 (2008)
Issue (Month): 3 (March)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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CeMMAP working papers
CWP14/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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