Article ID Journal Published Year Pages File Type
1148246 Journal of Statistical Planning and Inference 2009 12 Pages PDF
Abstract

In this paper we revisit the classical problem of interval estimation for one-binomial parameter and for the log odds ratio of two binomial parameters. We examine the confidence intervals provided by two versions of the modified log likelihood root: the usual Barndorff-Nielsen's r*r* and a Bayesian version of the r*r* test statistic.For the one-binomial problem, this work updates the findings of Brown et al. [2003. Interval estimation in exponential families. Statistica Sinica 13, 19–49; 2002. Confidence intervals for a binomial proportion and asymptotic expansion. The Annals of Statistics 30, 160–201] and Cai [2005. One-sided confidence intervals in discrete distributions. Journal of Statistical Planning and Inference 131, 63–88] to higher-order methods. For the log odds ratio of two binomial parameters we show via Edgeworth expansion that both versions of the r*r* statistics give confidence intervals which nearly completely eliminate the systematic bias in the unconditional smooth coverage probability. We also give expansions for the length of the confidence intervals.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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