Fiducial generalized confidence intervals
Fiducial generalized confidence intervals
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DOI：
10.1198/016214505000000736
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发表时间：
2006-03-01
影响因子：
3.7
通讯作者：
Patterson, P
中科院分区：
文献类型：
--
作者：
Hannig, J;Iyer, H;Patterson, P
广义关键量（GPQs）和广义置信区间（GCI）已被证明是在许多实际问题中进行推理的有用工具。虽然不能保证GCI具有精确的频率覆盖率，但一些已发表和未发表的模拟研究表明，这些区间的覆盖概率足够接近其标称值，以便在实践中有用。在这篇文章中，我们挑选出一个子类的广义枢轴量，我们称之为基准广义枢轴量（FGPQs），并表明，在一些温和的条件下，GCI构造使用FGPQs有正确的频率覆盖，至少渐近。我们描述了三种一般的方法来构建FGPQs-一个配方的基础上可逆的枢轴关系，和它的两个扩展，并证明了它们的有用性，推导出一些以前未知的GPQs和GCls。公平地说，几乎所有已发表的GCI都可以使用这些配方之一来获得。作为一个有趣的副产品，我们的调查，我们注意到，子家庭的基准广义枢轴有一个密切的联系，基准推理提出的R。A.费希尔这就是为什么我们把提出的广义枢轴称为基准广义枢轴量。我们用几个例子来证明这些概念。
Generalized pivotal quantities (GPQs) and generalized confidence intervals (GCIs) have proven to be useful tools for making inferences in many practical problems. Although GCIs are not guaranteed to have exact frequentist coverage, a number of published and unpublished simulation studies suggest that the coverage probabilities of such intervals are sufficiently close to their nominal value so as to be useful in practice. In this article we single out a subclass of generalized pivotal quantities, which we call fiducial generalized pivotal quantities (FGPQs), and show that under some mild conditions, GCIs constructed using FGPQs have correct frequentist coverage, at least asymptotically. We describe three general approaches for constructing FGPQs-a recipe based on invertible pivotal relationships, and two extensions of it-and demonstrate their usefulness by deriving some previously unknown GPQs and GCls. It is fair to say that nearly every published GCI can be obtained using one of these recipes. As an interesting byproduct of our investigations, we note that the subfamily of fiducial generalized pivots has a close connection with fiducial inference proposed by R. A. Fisher. This is why we refer to the proposed generalized pivots as fiducial generalized pivotal quantities. We demonstrate these concepts using several examples.