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 Estimation of a probability with optimum guaranteed confidence in inverse binomial sampling
 摘  要: 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 $\mu_1$, $\mu_2$.
 发  表: 2008

 共享有3个版本 http://arxiv.org/abs/0809.2402 http://projecteuclid.org/euclid.bj/1274821081 http://www.e-publications.org/ims/submission/index.php/BEJ/user/submissionFile/3907?confirm=a141f040
 Bibtex @article{ author = {Luis Mendo and E M. HERNANDO}, title = {Estimation of a probability with optimum guaranteed confidence in inverse binomial sampling}, year = {2008}, doi = {10.3150/09-BEJ219} }

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