标题： 一致的二次型比值的鞍点近似 显示英文标题

标题： Uniform saddlepoint approximations for ratios of quadratic forms

摘要： 考虑了引入非中心性的二次型的比值，其中分子和分母是相关正态变量的二次型。假设分母几乎处处为正。 最小二乘法、Yule-Walker 方法、Burg 方法以及 Durbin-Watson 统计量等不同序列相关性估计提供了此类比值的重要实例。 此类比值的累积分布函数（c.d.f.）和密度可以采用尖点逼近方法。 这些逼近方法被证明在整个支持范围内保持相对误差的一致性。 此外，还推导出了在支持极端边缘处极限相对误差的显式值。 显示英文摘要

摘要： 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.