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Asymptotic infimum coverage probability for interval estimation of proportions

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  • Weizhen Wang
  • Zhongzhan Zhang

Abstract

In this paper, we discuss asymptotic infimum coverage probability (ICP) of eight widely used confidence intervals for proportions, including the Agresti–Coull (A–C) interval (Am Stat 52:119–126, 1998 ) and the Clopper–Pearson (C–P) interval (Biometrika 26:404–413, 1934 ). For the A–C interval, a sharp upper bound for its asymptotic ICP is derived. It is less than nominal for the commonly applied nominal values of 0.99, 0.95 and 0.9 and is equal to zero when the nominal level is below 0.4802. The $$1-\alpha $$ 1 - α C–P interval is known to be conservative. However, we show through a brief numerical study that the C–P interval with a given average coverage probability $$1-\gamma $$ 1 - γ typically has a similar or larger ICP and a smaller average expected length than the corresponding A–C interval, and its ICP approaches to $$1-\gamma $$ 1 - γ when the sample size goes large. All mathematical proofs and R-codes for computation in the paper are given in Supplementary Materials. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Weizhen Wang & Zhongzhan Zhang, 2014. "Asymptotic infimum coverage probability for interval estimation of proportions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(5), pages 635-646, July.
    • Handle: RePEc:spr:metrik:v:77:y:2014:i:5:p:635-646
    DOI: 10.1007/s00184-013-0457-5
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    References listed on IDEAS

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    1. Huwang, Longcheen, 1995. "A note on the accuracy of an approximate interval for the binomial parameter," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 177-180, August.
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    Cited by:

    1. Wang, Weizhen, 2017. "On exact interval estimation for the odds ratio in subject-specific table," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 360-366.

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