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The Distribution of a Ratio of Quadratic Forms in Noncentral Normal Variables

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  • Giovanni Forchini

Abstract

An expression for the exact cumulative distribution function of a ratio of quadratic forms in noncentral normal variable is derived in terms of infinite series of top order invariant polynomials.

Suggested Citation

  • Giovanni Forchini, "undated". "The Distribution of a Ratio of Quadratic Forms in Noncentral Normal Variables," Discussion Papers 01/12, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:01/12
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    File URL: https://www.york.ac.uk/media/economics/documents/discussionpapers/2001/0112.pdf
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    References listed on IDEAS

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    1. Forchini, G., 2002. "The Exact Cumulative Distribution Function Of A Ratio Of Quadratic Forms In Normal Variables, With Application To The Ar(1) Model," Econometric Theory, Cambridge University Press, vol. 18(4), pages 823-852, August.
    2. Phillips, P C B, 1986. "The Exact Distribution of the Wald Statistic," Econometrica, Econometric Society, vol. 54(4), pages 881-895, July.
    3. Chikuse, Yasuko, 1987. "Methods for Constructing Top Order Invariant Polynomials," Econometric Theory, Cambridge University Press, vol. 3(2), pages 195-207, April.
    4. Marsh, Patrick W.N., 1998. "Saddlepoint Approximations For Noncentral Quadratic Forms," Econometric Theory, Cambridge University Press, vol. 14(5), pages 539-559, October.
    5. Hillier, G.H., 1999. "The density of a quadratic form in a vector uniformly distributed on the n-sphere," Discussion Paper Series In Economics And Econometrics 9902, Economics Division, School of Social Sciences, University of Southampton.
    6. Marsh, P., 1995. "Saddlepoint approximations and non-central quadratic forms," Discussion Paper Series In Economics And Econometrics 9530, Economics Division, School of Social Sciences, University of Southampton.
    7. Hillier, Grant, 2001. "THE DENSITY OF A QUADRATIC FORM IN A VECTOR UNIFORMLY DISTRIBUTED ON THE n-SPHERE," Econometric Theory, Cambridge University Press, vol. 17(1), pages 1-28, February.
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    Cited by:

    1. Salcedo, Gladys E. & Porto, Rogério F. & Morettin, Pedro A., 2012. "Comparing non-stationary and irregularly spaced time series," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3921-3934.
    2. Grant Hillier & Federico Martellosio, 2013. "Properties of the maximum likelihood estimator in spatial autoregressive models," CeMMAP working papers CWP44/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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    Keywords

    Ratio of quadratic forms; quadratic forms in normal variables.;

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