Ensemble confidence intervals for binomial proportions

Abstract

We propose two measures of performance for a confidence interval for a binomial proportion p: the root mean squared error and the mean absolute deviation. We also devise a confidence interval for p based on the actual coverage function that combines several existing approximate confidence intervals. This "Ensemble" confidence interval has improved statistical properties over the constituent confidence intervals. Software in an R package, which can be used in devising and assessing these confidence intervals, is available on CRAN.