Uniform saddlepoint approximations for ratios of quadratic forms

Details Uniform saddlepoint approximations for ratios of quadratic forms Uniform saddlepoint approximations for ratios of quadratic forms

2008-03-14

arxiv.org/abs/0803.2132v1

Bernoulli 2008, Vol. 14, No. 1, 140-154

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/07-BEJ6169 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ6169

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.

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