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Coverage-adjusted Confidence Intervals for a Binomial Proportion

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  • Måns Thulin

Abstract

type="main" xml:id="sjos12021-abs-0001"> We consider the classic problem of interval estimation of a proportion p based on binomial sampling. The ‘exact’ Clopper–Pearson confidence interval for p is known to be unnecessarily conservative. We propose coverage adjustments of the Clopper–Pearson interval that incorporate prior or posterior beliefs into the interval. Using heatmap-type plots for comparing confidence intervals, we show that the coverage-adjusted intervals have satisfying coverage and shorter expected lengths than competing intervals found in the literature.

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  • Måns Thulin, 2014. "Coverage-adjusted Confidence Intervals for a Binomial Proportion," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 291-300, June.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:2:p:291-300
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    File URL: http://hdl.handle.net/10.1111/sjos.12021
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    References listed on IDEAS

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    1. Cai, Yong & Krishnamoorthy, K., 2005. "A simple improved inferential method for some discrete distributions," Computational Statistics & Data Analysis, Elsevier, vol. 48(3), pages 605-621, March.
    2. Alan Hutson, 2006. "Modifying the exact test for a binomial proportion and comparisons with other approaches," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(7), pages 679-690.
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