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Asymptotic infimum coverage probability for interval estimation of proportions

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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 \(1-\alpha \) 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 \(1-\gamma \) typically has a similar or larger ICP and a smaller average expected length than the corresponding A–C interval, and its ICP approaches to \(1-\gamma \) when the sample size goes large. All mathematical proofs and R-codes for computation in the paper are given in Supplementary Materials.

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Acknowledgments

The first author was partially supported by NSF (US) Grant No. DMS-0906858. The second author was partially supported by NSFC Grant No. 10971007. The authors are grateful to an Associate Editor for the helpful comments.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Wright State University, Dayton, OH, 45435, USA

    Weizhen Wang

  2. College of Applied Sciences, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Weizhen Wang & Zhongzhan Zhang

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  1. Weizhen Wang
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  2. Zhongzhan Zhang
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Correspondence to Weizhen Wang.

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Wang, W., Zhang, Z. Asymptotic infimum coverage probability for interval estimation of proportions. Metrika 77, 635–646 (2014). https://doi.org/10.1007/s00184-013-0457-5

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  • DOI: https://doi.org/10.1007/s00184-013-0457-5

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