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Mean-Minimum Exact Confidence Intervals

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  • Joseph B. Lang

Abstract

This article introduces mean-minimum (MM) exact confidence intervals for a binomial probability. These intervals guarantee that both the mean and the minimum frequentist coverage never drop below specified values. For example, an MM 95[93]% interval has mean coverage at least 95% and minimum coverage at least 93%. In the conventional sense, such an interval can be viewed as an exact 93% interval that has mean coverage at least 95% or it can be viewed as an approximate 95% interval that has minimum coverage at least 93%. Graphical and numerical summaries of coverage and expected length suggest that the Blaker-based MM exact interval is an attractive alternative to, even an improvement over, commonly recommended approximate and exact intervals, including the Agresti–Coull approximate interval, the Clopper–Pearson (CP) exact interval, and the more recently recommended CP-, Blaker-, and Sterne-based mean-coverage-adjusted approximate intervals.

Suggested Citation

  • Joseph B. Lang, 2017. "Mean-Minimum Exact Confidence Intervals," The American Statistician, Taylor & Francis Journals, vol. 71(4), pages 354-368, October.
    • Handle: RePEc:taf:amstat:v:71:y:2017:i:4:p:354-368
    DOI: 10.1080/00031305.2016.1256838
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    References listed on IDEAS

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    1. Agresti, Alan & Gottard, Anna, 2007. "Nonconservative exact small-sample inference for discrete data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6447-6458, August.
    2. Mark F. Schilling & Jimmy A. Doi, 2014. "A Coverage Probability Approach to Finding an Optimal Binomial Confidence Procedure," The American Statistician, Taylor & Francis Journals, vol. 68(3), pages 133-145, February.
    3. Alan Agresti & Yongyi Min, 2001. "On Small-Sample Confidence Intervals for Parameters in Discrete Distributions," Biometrics, The International Biometric Society, vol. 57(3), pages 963-971, September.
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    Cited by:

    1. Sascha Wörz & Heinz Bernhardt, 2020. "Towards an uniformly most powerful binomial test," Statistical Papers, Springer, vol. 61(5), pages 2149-2156, October.

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