Interval estimation for a binomial proportion - Comment - Rejoinder

被引：2480

作者：

Brown, LD

Cai, TT

DasGupta, A

Agresti, A

Coull, BA

Casella, G

Corcoran, C

Mehta, C

Ghosh, M

Santner, TJ

Brown, LD

Cai, TT

DasGupta, A

机构：

[1] Univ Penn, Wharton Sch, Philadelphia, PA 19104 USA

[2] Purdue Univ, Dept Stat, W Lafayette, IN 47907 USA

来源：

STATISTICAL SCIENCE | 2001年 / 16卷 / 02期

关键词：

Bayes; binomial distribution; confidence intervals; coverage probability; Edgeworth expansion; expected length; Jeffreys prior; normal approximation; posterior;

D O I：

10.1214/ss/1009213286

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：101 / 133

页数：33

共 57 条

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