%0 Journal Article
%T Estimation of a probability with optimum guaranteed confidence in inverse binomial sampling
%A Luis Mendo
%A Jos¨¦ M. Hernando
%J Mathematics
%D 2008
%I arXiv
%R 10.3150/09-BEJ219
%X 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 $\hat{p}$ is measured by the confidence level $P[p/\mu_2\leq\hat{p}\leq p\mu_1]$. The confidence levels $c_0$ that can be guaranteed for $p$ unknown, that is, such that $P[p/\mu_2\leq \hat{p}\leq p\mu_1]\geq c_0$ for all $p\in(0,1)$, are investigated. It is shown that within the general class of randomized or non-randomized estimators based on inverse binomial sampling, there is a maximum $c_0$ that can be guaranteed for arbitrary $p$. A non-randomized estimator is given that achieves this maximum guaranteed confidence under mild conditions on $\mu_1$, $\mu_2$.
%U http://arxiv.org/abs/0809.2402v4