Interval estimation for a binomial proportion - Comment - Rejoinder
Interval estimation for a binomial proportion - Comment - Rejoinder
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DOI：
10.1214/ss/1009213286
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发表时间：
2001-05-01
影响因子：
5.7
通讯作者：
DasGupta, A
中科院分区：
文献类型：
--
作者：
Brown, LD;Cai, TT;DasGupta, A
我们重新审视二项式比例的区间估计问题。标准 Wald 置信区间的覆盖概率的不稳定行为先前已在文献中评论过（Blyth 和 Still、Agresti 和 Coull、Santner 等）。我们首先表明 Wald 区间的混沌覆盖特性比我们想象的要持久得多。此外，关于其安全性的常见教科书处方在多个方面具有误导性和缺陷，不能被信任。这导致我们考虑替代间隔。提出了许多自然的替代方案，每种方案都有其动机和背景。检查每个间隔的覆盖概率和长度。基于此分析，对于较小的 n，我们建议使用 Wilson 区间或等尾 Jeffreys 先验区间，对于较大的 n，建议使用 Agresti 和 Coull 中建议的区间。我们还为使用杰弗里斯间隔提供了额外的频率论理由。
We revisit the problem of interval estimation of a binomial proportion. The erratic behavior of the coverage probability of the standard Wald confidence interval has previously been remarked on in the literature (Blyth and Still, Agresti and Coull, Santner and others). We begin by showing that the chaotic coverage properties of the Wald interval are far more persistent than is appreciated. Furthermore, common textbook prescriptions regarding its safety are misleading and defective in several respects and cannot be trusted.This leads us to consideration of alternative intervals. A number of natural alternatives are presented, each with its motivation and context. Each interval is examined for its coverage probability and its length. Based on this analysis, we recommend the Wilson interval or the equal-tailed Jeffreys prior interval for small n and the interval suggested in Agresti and Coull for larger n. We also provide an additional frequentist justification for use of the Jeffreys interval.