A note on confidence interval estimation for a linear function of binomial proportions

The Wilson score confidence interval for a binomial proportion has been widely applied in practice, due largely to its good performance in finite samples and its simplicity in calculation. We propose its use in setting confidence limits for a linear function of binomial proportions using the method of variance estimates recovery. Exact evaluation results show that this approach provides intervals that are narrower than the ones based on the adjusted Wald interval while aligning the mean coverage with the nominal level.