On the expectation of a ratio of quadratic forms in normal variables

Murray D. Smith

doi:10.1016/0047-259X(89)90065-1

On the expectation of a ratio of quadratic forms in normal variables

Murray D. Smith^*

^*Awdur cyfatebol y gwaith hwn

University of Sydney

Allbwn ymchwil: Cyfraniad at gyfnodolyn › Erthygl › adolygiad gan gymheiriaid

7 Wedi eu Llwytho i Lawr (Pure)

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Using relatively recent results from multivariate distribution theory, the expectation of a ratio of quadratic forms in normal variables is obtained. Infinite series expressions involving the invariant polynomials of matrix argument are derived. Convergence of the solution depends upon the choice made for two positive, but upper bounded, constants. The same methodology is used to obtain the expectation of multiple ratios of quadratic forms in normal variables.

Iaith wreiddiol	Saesneg
Tudalennau (o-i)	244-257
Nifer y tudalennau	14
Cyfnodolyn	Journal of Multivariate Analysis
Cyfrol	31
Rhif cyhoeddi	2
Dynodwyr Gwrthrych Digidol (DOIs)	https://doi.org/10.1016/0047-259X(89)90065-1
Statws	Cyhoeddwyd - 01 Tach 1989
Cyhoeddwyd yn allanol	Ie

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10.1016/0047-259X(89)90065-1Trwydded: Arall

ArticleFersiwn derfynol wedi’i chyhoeddi, 668 KBTrwydded: Arall

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title = "On the expectation of a ratio of quadratic forms in normal variables",

abstract = "Using relatively recent results from multivariate distribution theory, the expectation of a ratio of quadratic forms in normal variables is obtained. Infinite series expressions involving the invariant polynomials of matrix argument are derived. Convergence of the solution depends upon the choice made for two positive, but upper bounded, constants. The same methodology is used to obtain the expectation of multiple ratios of quadratic forms in normal variables.",

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N2 - Using relatively recent results from multivariate distribution theory, the expectation of a ratio of quadratic forms in normal variables is obtained. Infinite series expressions involving the invariant polynomials of matrix argument are derived. Convergence of the solution depends upon the choice made for two positive, but upper bounded, constants. The same methodology is used to obtain the expectation of multiple ratios of quadratic forms in normal variables.

AB - Using relatively recent results from multivariate distribution theory, the expectation of a ratio of quadratic forms in normal variables is obtained. Infinite series expressions involving the invariant polynomials of matrix argument are derived. Convergence of the solution depends upon the choice made for two positive, but upper bounded, constants. The same methodology is used to obtain the expectation of multiple ratios of quadratic forms in normal variables.

KW - generalized hypergeometric function

KW - invariant polynomials

KW - quadratic forms

KW - zonal polynomials

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U2 - 10.1016/0047-259X(89)90065-1

DO - 10.1016/0047-259X(89)90065-1

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On the expectation of a ratio of quadratic forms in normal variables

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