Some remarks on confidence or fiducial limits

Sterne, T. E.

doi:10.1093/biomet/41.1-2.275

Cited by 81 publications

(75 citation statements)

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“…acceptance curve of minimal span for that p. (In the case when two acceptance curves of minimal span each have maximal height, we assign to p the one with the higher l and u values to maintain half-open intervals of the form [,).) This turns out to be equivalent to a method proposed by Sterne (1954) under an entirely different rationale. In the language of acceptance curves, Sterne's approach was to construct acceptance intervals for each p by entering the values of x in decreasing order of their chance of being observed until AC l u (p) ≥ 1 − α.…”

Section: The Search For An Optimal Binomial Confidence Proceduresmentioning

confidence: 94%

A Coverage Probability Approach to Finding an Optimal Binomial Confidence Procedure

Schilling¹,

Doi²

2014

The American Statistician

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The problem of finding confidence intervals for the success parameter of a binomial experiment has a long history, and a myriad of procedures have been developed. Most exploit the duality between hypothesis testing and confidence regions and are typically based on large sample approximations. We instead employ a direct approach that attempts to determine the optimal coverage probability function a binomial confidence procedure can have from the exact underlying binomial distributions, which in turn defines the associated procedure. We show that a graphical perspective provides much insight into the problem. Both procedures whose coverage never falls below the declared confidence level and those that achieve that level only approximately are analyzed. We introduce the Length/Coverage Optimal method, a variant of Sterne's procedure that minimizes average length while maximizing coverage among all length minimizing procedures, and show that it is superior in important ways to existing procedures.

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Section: The Search For An Optimal Binomial Confidence Proceduresmentioning

confidence: 94%

A Coverage Probability Approach to Finding an Optimal Binomial Confidence Procedure

Schilling¹,

Doi²

2014

The American Statistician

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“…C h0 can be considered as the two-dimensional generalization of that proposed by Sterne [19] for a single binomial proportion. Let P h0 (C h0 ) denote the probability of C h0 under h 0 , and let M = max{P h0 (C h0 ), h 0 ∈ H 0 }.…”

Section: Methodsmentioning

confidence: 99%

Exact inference for the risk ratio with an imperfect diagnostic test

Reiczigel

Singer²,

Láng

2016

Epidemiol. Infect.

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SUMMARYThe risk ratio quantifies the risk of disease in a study population relative to a reference population. Standard methods of estimation and testing assume a perfect diagnostic test having sensitivity and specificity of 100%. However, this assumption typically does not hold, and this may invalidate naive estimation and testing for the risk ratio. We propose procedures that control for sensitivity and specificity of the diagnostic test, given the risks are measured by proportions, as it is in crosssectional studies or studies with fixed follow-up times. These procedures provide an exact unconditional test and confidence interval for the true risk ratio. The methods also cover the case when sensitivity and specificity differ in the two groups (differential misclassification). The resulting test and confidence interval may be useful in epidemiological studies as well as in clinical and vaccine trials. We illustrate the method with real-life examples which demonstrate that ignoring sensitivity and specificity of the diagnostic test may lead to considerable bias in the estimated risk ratio.

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“…Blyth and Still (1983) investigated the performance of W, WCC, CP, Sterne's binomial confidence interval method (Sterne, 1954), and Pratt's (P) approximate confidence interval method (Pratt, 1968). Their results demonstrate the need for a continuity correction even when n is large.…”

Section: Methodsmentioning

confidence: 99%

Better Binomial Confidence Intervals

Reed

2007

J. Mod. App. Stat. Meth.

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The construction of a confidence interval for a binomial parameter is a basic analysis in statistical inference. Most introductory statistics textbook authors present the binomial confidence interval based on the asymptotic normality of the sample proportion and estimating the standard error -the Wald method. For the one sample binomial confidence interval the Clopper-Pearson exact method has been regarded as definitive as it eliminates both overshoot and zero width intervals. The Clopper-Pearson exact method is the most conservative and is unquestionably a better alternative to the Wald method. Other viable alternatives include Wilson's Score, the Agresti-Coull method, and the Borkowf SAIFS-z.

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Some remarks on confidence or fiducial limits

Cited by 81 publications

References 1 publication

A Coverage Probability Approach to Finding an Optimal Binomial Confidence Procedure

A Coverage Probability Approach to Finding an Optimal Binomial Confidence Procedure

Exact inference for the risk ratio with an imperfect diagnostic test

Better Binomial Confidence Intervals

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