
A New Exact Confidence Interval for the Difference of Two Binomial Proportions
We consider interval estimation of the difference between two binomial p...
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Construction of Confidence Intervals
Introductory texts on statistics typically only cover the classical "two...
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On the lengths of tbased confidence intervals
Given n=mk iid samples from N(θ,σ^2) with θ and σ^2 unknown, we have two...
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Binomial confidence intervals for rare events: importance of defining margin of error relative to magnitude of proportion
Confidence interval performance is typically assessed in terms of two cr...
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Robust statistical inference for the matched net benefit and the matched win ratio using prioritized composite endpoints
As alternatives to the timetofirstevent analysis of composite endpoin...
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Mathematical properties and finitepopulation correction for the Wilson score interval
In this paper we examine the properties of the Wilson score interval, us...
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Adaptive Inferential Method for Monotone Graph Invariants
We consider the problem of undirected graphical model inference. In many...
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Locally correct confidence intervals for a binomial proportion: A new criteria for an interval estimator
Wellrecommended methods of forming `confidence intervals' for a binomial proportion give interval estimates that do not actually meet the definition of a confidence interval, in that their coverages are sometimes lower than the nominal confidence level. The methods are favoured because their intervals have a shorter average length than the ClopperPearson (goldstandard) method, whose intervals really are confidence intervals. Comparison of such methods is tricky – the best method should perhaps be the one that gives the shortest intervals (on average), but when is the coverage of a method so poor that it should not be classed as a means of forming confidence intervals? As the definition of a confidence interval is not being adhered to, another criterion for forming interval estimates for a binomial proportion is needed. In this paper we suggest a new criterion; methods which meet the criterion are said to yield locally correct confidence intervals. We propose a method that yields such intervals and prove that its intervals have a shorter average length than those of any other method that meets the criterion. Compared with the ClopperPearson method, the proposed method gives intervals with an appreciably smaller average length. The midp method also satisfies the new criterion and has its own optimality property.
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