Estimation of a probability with optimum guaranteed confidence in inverse binomial sampling

Sequential estimation of a probability p by means of inverse binomial sampling is considered. For mu_1, mu_2 > 1 given, the accuracy of an estimator p^ is measured by the confidence level Pr[p/mu_2 = c_0 for all p in (0,1), are investigated. It is shown that, within the general class of randomized or nonrandomized estimators based on inverse binomial sampling, there is a maximum c_0 that can be guaranteed for p arbitrary. A nonrandomized estimator is given that achieves this maximum guaranteed confidence under mild conditions on mu_1, mu_2.