On construction of the smallest one-sided confidence interval for the difference of two proportions. (English) Zbl 1183.62054

Wang, Weizhen

Ann. Stat. 38, No. 2, 1227-1243 (2010).

Summary: For any class of one-sided \(1 - \alpha \) confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the difference of two proportions of two independent binomial random variables, is constructed based on a direct analysis of the coverage probability function. A special ordering on the confidence limit is developed and the corresponding smallest confidence interval is derived. This interval is then applied to identify the minimum effective dose (MED) for binary data in dose-response studies, and a multiple test procedure that controls the familywise error rate at level \(\alpha \) is obtained. A generalization of constructing the smallest one-sided confidence interval to other discrete sample spaces is discussed in the presence of nuisance parameters.

MSC:

62F25	Parametric tolerance and confidence regions
62J15	Paired and multiple comparisons; multiple testing
62P10	Applications of statistics to biology and medical sciences; meta analysis

Keywords:

binomial distribution; coverage probability; minimum effective dose; multiple tests; Poisson distribution; set inclusion

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