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

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Author Info
Giovanni Forchini

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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.

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Paper provided by Department of Economics, University of York in its series Discussion Papers with number 01/12.

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Handle: RePEc:yor:yorken:01/12

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Postal: Department of Economics and Related Studies, University of York, York, YO10 5DD, United Kingdom
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Keywords: Ratio of quadratic forms; quadratic forms in normal variables.;

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  1. Phillips, P C B, 1986. "The Exact Distribution of the Wald Statistic," Econometrica, Econometric Society, vol. 54(4), pages 881-95, July. [Downloadable!] (restricted)
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  2. Chikuse, Yasuko, 1987. "Methods for Constructing Top Order Invariant Polynomials," Econometric Theory, Cambridge University Press, vol. 3(02), pages 195-207, April. [Downloadable!]
  3. Marsh, Patrick W.N., 1998. "Saddlepoint Approximations For Noncentral Quadratic Forms," Econometric Theory, Cambridge University Press, vol. 14(05), pages 539-559, October. [Downloadable!]
  4. 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(01), pages 1-28, February. [Downloadable!]
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  5. Giovanni Forchini, . "The Exact Cumulative Distribution Function of a Ratio of Quadratic Forms in Normal Variables with Application to the AR(1) Model," Discussion Papers 01/02, Department of Economics, University of York. [Downloadable!]
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