title: Smooth bootstrap-based confidence intervals for one binomial proportion and difference of two proportions.
abstract: Constructing confidence intervals (CIs) for a binomial proportion and the difference between two binomial proportions is a fundamental and well-studied problem with respect to the analysis of binary data. In this note, we propose a new bootstrap procedure to estimate the CIs by resampling from a newly developed smooth quantile function in [11] for discrete data. We perform a variety of simulation studies in order to illustrate the strong performance of our approach. The coverage probabilities of our CIs in the one-sample setting are superior than or comparable to other well-known approaches. The true utility of our new and novel approach is in the two-sample setting. For the difference of two proportions, our smooth bootstrap CIs provide better coverage probabilities almost uniformly over the interval (-1, 1), particularly in the tail region as compared than other published methods included in our simulation. We illustrate our methodology via an application to several different binary data sets.
authors.affiliation: Department of Public Health and Preventive Medicine, State University of New York Upstate Medical University, 750 East Adams Street, Syracuse, NY 13210, USA.
authors.forename: Dongliang
authors.initials: D
authors.lastname: Wang
authors.affiliation: Department of Biostatistics, University at Buffalo, 3435 Main St., Buffalo, NY 14214-3000, USA.
authors.forename: Alan D
authors.initials: AD
authors.lastname: Hutson
keywords: binary data; bootstrap; confidence interval; proportion; quantile function