Bernoulli

  • Bernoulli
  • Volume 14, Number 1 (2008), 140-154.

Uniform saddlepoint approximations for ratios of quadratic forms

Ronald W. Butler and Marc S. Paolella

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Abstract

Ratios of quadratic forms in correlated normal variables which introduce noncentrality into the quadratic forms are considered. The denominator is assumed to be positive (with probability 1). Various serial correlation estimates such as least-squares, Yule–Walker and Burg, as well as Durbin–Watson statistics, provide important examples of such ratios. The cumulative distribution function (c.d.f.) and density for such ratios admit saddlepoint approximations. These approximations are shown to preserve uniformity of relative error over the entire range of support. Furthermore, explicit values for the limiting relative errors at the extreme edges of support are derived.

Article information

Source
Bernoulli, Volume 14, Number 1 (2008), 140-154.

Dates
First available in Project Euclid: 8 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.bj/1202492788

Digital Object Identifier
doi:10.3150/07-BEJ6169

Mathematical Reviews number (MathSciNet)
MR2401657

Zentralblatt MATH identifier
1155.62009

Keywords
ratios of quadratic forms saddlepoint approximations serial correlations

Citation

Butler, Ronald W.; Paolella, Marc S. Uniform saddlepoint approximations for ratios of quadratic forms. Bernoulli 14 (2008), no. 1, 140--154. doi:10.3150/07-BEJ6169. https://projecteuclid.org/euclid.bj/1202492788


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