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

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  • Smith, Murray D.

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.

Suggested Citation

  • Smith, Murray D., 1989. "On the expectation of a ratio of quadratic forms in normal variables," Journal of Multivariate Analysis, Elsevier, vol. 31(2), pages 244-257, November.
    • Handle: RePEc:eee:jmvana:v:31:y:1989:i:2:p:244-257
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    Citations

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    Cited by:

    1. Hillier, Grant & Kan, Raymond & Wang, Xiaolu, 2009. "Computationally Efficient Recursions For Top-Order Invariant Polynomials With Applications," Econometric Theory, Cambridge University Press, vol. 25(1), pages 211-242, February.
    2. Rukhin, Andrew L., 2009. "Identities for negative moments of quadratic forms in normal variables," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1004-1007, April.
    3. Poskitt, D.S. & Grose, Simone D. & Martin, Gael M., 2015. "Higher-order improvements of the sieve bootstrap for fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 188(1), pages 94-110.
    4. Grant Hillier & Raymond Kan & Xiaolu Wang, 2008. "Generating functions and short recursions, with applications to the moments of quadratic forms in noncentral normal vectors," CeMMAP working papers CWP14/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Hillier, Grant & Kan, Raymond & Wang, Xiaoulu, 2009. "Generating functions and short recursions, with applications to the moments of quadratic forms in noncentral normal vectors," Discussion Paper Series In Economics And Econometrics 918, Economics Division, School of Social Sciences, University of Southampton.
    6. Bao, Yong & Kan, Raymond, 2013. "On the moments of ratios of quadratic forms in normal random variables," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 229-245.
    7. Munir Mahmood & Maxwell L. King, 2016. "On solving bias-corrected non-linear estimation equations with an application to the dynamic linear model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(4), pages 332-355, November.
    8. Hillier, Grant & Kan, Raymond & Wang, Xiaoulu, 2009. "Generating functions and short recursions, with applications to the moments of quadratic forms in noncentral normal vectors," Discussion Paper Series In Economics And Econometrics 0918, Economics Division, School of Social Sciences, University of Southampton.

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