Existence of unbiased estimates in sequential binomial experiments

Abstract

For sequential Bernoulli trials, a necessary condition for a parametric function to be unbiasedly estimable is that it be continuous. Depending on the existence of the moments of the corresponding stopping time and the estimator, these functions are differentiable up to a given order. We also study the implications of these results to the problem of estimating min (p, 1-p) unbiasedly.