Unbiased Monte Carlo estimator with guaranteed confidence

Abstract

This paper considers the uniformly minimum variance unbiased estimator of a probability p based on inverse binomial sampling. It is shown that the confidence associated to intervals of the form [p/mu₂, pmu₁], mu₁, mu₂ > 1 has an asymptotic value as p rarr 0. Furthermore, the confidence for p isin (0, 1) arbitrary is guaranteed to exceed this asymptotic value if mu₁, mu₂ satisfy certain conditions. The derived conditions cover a wide range of practical situations.