Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses

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dc.creatorMeinshausen, Nicolai
dc.creatorRice, John
dc.date2005-01-19
dc.date2006-05-18
dc.date.accessioned2026-07-07T08:06:39Z
dc.date.available2026-07-07T08:06:39Z
dc.descriptionWe consider the problem of estimating the number of false null hypotheses among a very large number of independently tested hypotheses, focusing on the situation in which the proportion of false null hypotheses is very small. We propose a family of methods for establishing lower $100(1-α)%$ confidence bounds for this proportion, based on the empirical distribution of the $p$-values of the tests. Methods in this family are then compared in terms of ability to consistently estimate the proportion by letting $α\to 0$ as the number of hypothesis tests increases and the proportion decreases. This work is motivated by a signal detection problem that occurs in astronomy.
dc.descriptionPublished at http://dx.doi.org/10.1214/009053605000000741 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0501289
dc.identifierhttp://arxiv.org/abs/math/0501289
dc.identifierAnnals of Statistics 2006, Vol. 34, No. 1, 373-393
dc.identifierdoi:10.1214/009053605000000741
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130678
dc.subjectStatistics Theory
dc.subject62H15 (Primary) 62J15, 62P35 (Secondary)
dc.titleEstimating the proportion of false null hypotheses among a large number of independently tested hypotheses
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