Uniform saddlepoint approximations for ratios of quadratic forms

  title={Uniform saddlepoint approximations for ratios of quadratic forms},
  author={Ronald W. Butler and Marc S. Paolella},
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… CONTINUE READING
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