Smooth bootstrap-based confidence intervals for one binomial proportion and difference of two proportions

Dongliang Wang and Alan Hutson

Journal of Applied Statistics, 2013, vol. 40, issue 3, 614-625

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.

Date: 2013
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DOI: 10.1080/02664763.2012.750283

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