Abstract
For a confidence interval (L(X),U(X)) of a parameter θ in one-parameter discrete distributions, the coverage probability is a variable function of θ. The confidence coefficient is the infimum of the coverage probabilities, inf θ P θ (θ∈(L(X),U(X))). Since we do not know which point in the parameter space the infimum coverage probability occurs at, the exact confidence coefficients are unknown. Beside confidence coefficients, evaluation of a confidence intervals can be based on the average coverage probability. Usually, the exact average probability is also unknown and it was approximated by taking the mean of the coverage probabilities at some randomly chosen points in the parameter space. In this article, methodologies for computing the exact average coverage probabilities as well as the exact confidence coefficients of confidence intervals for one-parameter discrete distributions are proposed. With these methodologies, both exact values can be derived.
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Agresti, A., Coull, B.A.: Approximate is better than “exact” for interval estimation of binomial proportions. Am. Stat. 52, 119–126 (1998)
Blyth, C.R., Still, H.A.: Binomial confidence intervals. J. Am. Stat. Assoc. 78, 108–116 (1983)
Brown, L.D., Cai, T., DasGupta, A.: Confidence intervals for a binomial and asymptotic expansions. Ann. Stat. 30, 160–201 (2002)
Brown, L.D., Cai, T., DasGupta, A.: Interval estimation in exponential families. Stat. Sin. 13, 19–49 (2003)
Clopper, C.J., Pearson, E.S.: The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26, 404–413 (1934)
Lehmann, E.L.: Testing Statistical Hypotheses, 2nd edn. Wiley, New York (1986)
Lehmann, E.L., Loh, W.Y.: Pointwise versus uniform robustness of some large-sample tests and confidence intervals. Scand. J. Stat. 17, 177–187 (1990)
Stein, C.: On the coverage probability of confidence sets based on a prior distribution. In: Sequential Methods in Statistics. Banach Center Publ., vol. 16, pp. 485–514. PWN, Warsaw (1985)
Wang, H.: The monotone bound property and the full coverage property of confidence intervals for a binomial proportion. Technical report (2006)
Wang, H.: Exact confidence coefficients of confidence intervals for a binomial proportion. Stat. Sin. 17, 361–368 (2007)
Woodroofe, M.: Very weak expansions for sequential confidence levels. Ann. Stat. 14, 1049–1067 (1986)
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Wang, H. Exact average coverage probabilities and confidence coefficients of confidence intervals for discrete distributions. Stat Comput 19, 139–148 (2009). https://doi.org/10.1007/s11222-008-9077-8
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DOI: https://doi.org/10.1007/s11222-008-9077-8