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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.

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File URL: http://www.york.ac.uk/media/economics/documents/discussionpapers/2001/0112.pdf
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Bibliographic Info

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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Web page: http://www.york.ac.uk/economics/
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Keywords: Ratio of quadratic forms; quadratic forms in normal variables.;

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References

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  1. 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.
  2. Phillips, P C B, 1986. "The Exact Distribution of the Wald Statistic," Econometrica, Econometric Society, vol. 54(4), pages 881-95, July.
  3. 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.
  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.
  5. Marsh, Patrick W.N., 1998. "Saddlepoint Approximations For Noncentral Quadratic Forms," Econometric Theory, Cambridge University Press, vol. 14(05), pages 539-559, October.
  6. Chikuse, Yasuko, 1987. "Methods for Constructing Top Order Invariant Polynomials," Econometric Theory, Cambridge University Press, vol. 3(02), pages 195-207, April.
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Cited by:
  1. Grant Hillier & Federico Martellosio, 2013. "Properties of the maximum likelihood estimator in spacial autoregressive models," CeMMAP working papers CWP44/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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