二次型比的一致鞍点逼近
Uniform saddlepoint approximations for ratios of quadratic forms
摘要：
考虑了正态变量相关的二次型的比值，它在二次型中引入了非中心性。假设分母为正（概率为1）。各种序列相关估计，如最小二乘法，尤尔-沃克和伯格，以及杜宾-沃森统计，提供了重要的例子，这样的比率。累积分布函数（c.d.f.）这样的比率和密度允许鞍点近似。这些近似被示出在整个支持范围内保持相对误差的均匀性。此外，明确的限制相对误差在极端边缘的支持。
英文摘要：
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.
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