Conndence Intervals for a Binomial Proportion and Edgeworth Expansions*
نویسنده
چکیده
We address the classic problem of interval estimation of a binomial proportion. The Wald interval ^ pz =2 n ?1=2 (^ p(1?^ p)) 1=2 is currently in near universal use. We rst 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. Fortunately, the asymptotic expansions are remarkably accurate at rather modest sample sizes, such as n = 40, or sometimes even n = 20. The expansions show that an interval suggested in Agresti and Coull (1998) dominates the score interval (Wilson (1927)), the Jeereys prior Bayesian interval, and also the standard interval in coverage probability. However, the asymptotic expansions for expected lengths show that the Agresti-Coull interval is always the longest of these, and the Jeereys prior interval is always the shortest among these. The standard interval and the Wilson interval, curiously, have identical second order expansions for their average expected length and are in between the Jeereys and the Agresti-Coull interval in the ranking for length. These analytical calculations support and complement the ndings and the recommendations in Brown, Cai and DasGupta (1999).
منابع مشابه
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تاریخ انتشار 1999