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On the Distribution of General Quadratic Functions in Normal Vectors

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  • M.C.M. de Gunst

Abstract

A representation in terms of independent standard normal variables tor the general quadratic form in normal variables in the univariate case, obtained by DIK and DE GUNST (1985), is extended to the multivariate situation. A representation for the quadratic function in normal vectors X'AX, where X is a random matrix with normally distributed elements and A a real symmetric matrix, is given in terms of independent and identically distributed central normal vectors. The representation is valid only when the covariance structure of X is of a special form, but all known results, especially necessary and sufficient conditions for X'AX to have a Wishart distribution, can easily be derived from it.

Suggested Citation

  • M.C.M. de Gunst, 1987. "On the Distribution of General Quadratic Functions in Normal Vectors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 41(4), pages 245-252, December.
    • Handle: RePEc:bla:stanee:v:41:y:1987:i:4:p:245-252
    DOI: 10.1111/j.1467-9574.1987.tb01217.x
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    Cited by:

    1. Hu, Jianhua, 2008. "Wishartness and independence of matrix quadratic forms in a normal random matrix," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 555-571, March.

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