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On matching confidence intervals and tests for some discrete distributions: methodological and computational aspects

Author

Listed:
  • Jan Klaschka

    (Institute of Computer Science of the Czech Academy of Sciences)

  • Jenő Reiczigel

    (University of Veterinary Medicine Budapest)

Abstract

Exact two-tailed tests and two-sided confidence intervals (CIs) for a binomial proportion or Poisson parameter by Sterne (Biometrika 41:117–129, 1954) or Blaker (Can J Stat 28(4):783–798, 2000) are successful in reducing conservatism of the Clopper–Pearson method. However, the methods suffer from an inconsistency between the tests and the corresponding CIs: In some cases, a parameter value is rejected by the test, though it lies in the CI. The problem results from non-unimodality of the test p value functions. We propose a slight modification of the tests that avoids the inconsistency, while preserving nestedness and exactness. Fast and accurate algorithms for both the test modification and calculation of confidence bounds are presented together with their theoretical background.

Suggested Citation

  • Jan Klaschka & Jenő Reiczigel, 2021. "On matching confidence intervals and tests for some discrete distributions: methodological and computational aspects," Computational Statistics, Springer, vol. 36(3), pages 1775-1790, September.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:3:d:10.1007_s00180-020-00986-0
    DOI: 10.1007/s00180-020-00986-0
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    References listed on IDEAS

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    1. Martin Andres, A. & Herranz Tejedor, I., 2004. "Exact unconditional non-classical tests on the difference of two proportions," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 373-388, March.
    2. Shalabh, 2006. "Exact Analysis of Discrete Data by K. F. Hirji," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(4), pages 1009-1009, October.
    3. 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.
    4. Reiczigel, Jeno & Abonyi-Tóth, Zsolt & Singer, Júlia, 2008. "An exact confidence set for two binomial proportions and exact unconditional confidence intervals for the difference and ratio of proportions," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 5046-5053, July.
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