We propose an optimal sequential methodology for obtaining confidence intervals for a binomial proportion θ. Assuming that an i.i.d. random sequence of Benoulli(θ) trials is observed sequentially, we are interested in designing a) a stopping time T that will decide when is the best time to stop sampling the process, and b) an optimum estimatorθ T that will provide the optimum center of the interval estimate of θ. We follow a semi-Bayesian approach, where we assume that there exists a prior distribution for θ, and our goal is to minimize the average number of samples while we guarantee a minimal coverage probability level. The solution is obtained by applying standard optimal stopping theory and computing the optimum pair (T,θ T ) numerically. Regarding the optimum stopping time component T , we demonstrate that it enjoys certain very uncommon characteristics not encountered in solutions of other classical optimal stopping problems. Finally, we compare our method with the optimum fixed-sample-size procedure but also with existing alternative sequential schemes.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.