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Improving The Numerical Technique For Computing The Accumulated Distribution Of A Quadratic Form In Normal Variables

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Author Info
Zeng-Hua Lu
Maxwell King
Abstract

This paper is concerned with the technique of numerically evaluating the cumulative distribution function of a quadratic form in normal variables. The efficiency of two new truncation bounds and all existing truncation bounds are investigated. We also find that the suggestion in the literature for further splitting truncation errors might reduce computational efficiency, and the optimum splitting rate could be different in different situations. A practical solution is provided. The paper also discusses a modified secant algorithm for finding the critical value of the distribution at any given significance level.

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File URL: http://www.informaworld.com/openurl?genre=article&doi=10.1081/ETC-120014346&magic=repec&7C&7C8674ECAB8BB840C6AD35DC6213A474B5
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Publisher Info
Article provided by Taylor and Francis Journals in its journal Econometric Reviews.

Volume (Year): 21 (2002)
Issue (Month): 2 ()
Pages: 149-165
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Handle: RePEc:taf:emetrv:v:21:y:2002:i:2:p:149-165

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Related research
Keywords: Quadratic form in normal variables; Numerical inversion of characteristic function; Truncation error; Newton'; s method; Secant method; JEL+Classification> JEL Classification; C19; C63;

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Dufour, Jean-Marie & King, Maxwell L., 1991. "Optimal invariant tests for the autocorrelation coefficient in linear regressions with stationary or nonstationary AR(1) errors," Journal of Econometrics, Elsevier, vol. 47(1), pages 115-143, January. [Downloadable!] (restricted)
  2. Ansley, Craig F. & Kohn, Robert & Shively, Thomas S., 1992. "Computing p-values for the generalized Durbin-Watson and other invariant test statistics," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 277-300. [Downloadable!] (restricted)
  3. King, Maxwell L., 1985. "A point optimal test for autoregressive disturbances," Journal of Econometrics, Elsevier, vol. 27(1), pages 21-37, January. [Downloadable!] (restricted)
  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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This page was last updated on 2009-12-10.

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