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

Abstract

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 $P[p/{\mu }_2\le \hat{p}\le p{\mu }_1]$. The confidence levels $c_0$ that can be guaranteed for $p$ unknown, that is, such that $P[p/{\mu }_2\le \hat{p}\le p{\mu }_1]\ge c_0$ 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 ${\mu }_1$, ${\mu }_2$.

Published in at http://dx.doi.org/10.3150/09-BEJ219 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

Cited by in corpus (4)

• Estimation of a Probability with Guaranteed Normalized Mean Absolute Error
• Asymptotically optimum estimation of a probability in inverse binomial sampling under general loss functions
• Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss
• A Theory of Truncated Inverse Sampling