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Zbl 1059.62533
Brown, Lawrence D.; Cai, T.Tony; DasGupta, Anirban
Interval estimation for a binomial proportion. (With comments and a rejoinder). (English)
[J] Stat. Sci. 16, No. 2, 101-133 (2001). ISSN 0883-4237

Summary: 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. \par 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 by Agresti and Coull for larger n. We also provide an additional frequentist justification for use of the Jeffreys interval.

MSC 2000:: *62F25 Parametric confidence regions, etc.

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

Cited in: Zbl 1157.62371 Zbl pre05374007

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