Confidence Intervals for a binomial proportion and asymptotic expansions
Confidence Intervals for a binomial proportion and asymptotic expansions
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DOI：
10.1214/aos/1015362189
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发表时间：
2002-02
影响因子：
4.5
通讯作者：
Lawrence D. Brown;Tommaso Cai;Anirban DasGupta
中科院分区：
文献类型：
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作者：
Lawrence D. Brown;Tommaso Cai;Anirban DasGupta
P±zα/2n−1/2(ˆp(1−ˆp))1/2目前几乎被普遍使用。我们首先证明了Wald区间的覆盖性质一直很差，并且挑战了几乎所有的传统智慧。然后，我们通过对它们的覆盖概率和期望长度的渐近展开，对标准区间和另外四个备选区间进行了理论比较。我们详细研究的另外四种区间方法分别是得分检验区间(Wilson)、似然比检验区间、Jeffreys先验贝叶斯区间和Gonsti和Coull提出的区间。覆盖率的渐近展开表明，这些替代方法中的前三种方法的覆盖率在名义值上下波动，而协议-库尔区间具有更大且更接近保守的覆盖率函数。对于五种区间方法，我们还渐近地考察了它们相对于p在(0，1)内支持的分布的平均覆盖率。在期望长度方面，渐近展开表明，协议-Coull区间总是其中最长的。除了p接近0或1之外，其余三个都相当可比，都比Wald间隔短。这些分析计算支持和补充了Brown，Cai和Dasgupta(统计学家)的结果和建议。SCI。(2001)16101-133)。
p ± zα/2n −1/2 ( ˆ p(1 −ˆ p)) 1/2 is currently in near universal use. We first show that the coverage properties of the Wald interval are persistently poor and defy virtually all conventional wisdom. We then proceed to a theoretical comparison of the standard interval and four additional alternative intervals by asymptotic expansions of their coverage probabilities and expected lengths. The four additional interval methods we study in detail are the score-test interval (Wilson), the likelihood-ratio-test interval, a Jeffreys prior Bayesian interval and an interval suggested by Agresti and Coull. The asymptotic expansions for coverage show that the first three of these alternative methods have coverages that fluctuate about the nominal value, while the Agresti– Coull interval has a somewhat larger and more nearly conservative coverage function. For the five interval methods we also investigate asymptotically their average coverage relative to distributions for p supported within (0, 1). In terms of expected length, asymptotic expansions show that the Agresti– Coull interval is always the longest of these. The remaining three are rather comparable and are shorter than the Wald interval except for p near 0 or 1. These analytical calculations support and complement the findings and the recommendations in Brown, Cai and DasGupta (Statist. Sci. (2001) 16 101–133).