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

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We 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.
Published 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)

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Statistics Theory, 62H15 (Primary) 62J15, 62P35 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/130678

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0501289
 http://arxiv.org/abs/math/0501289
 Annals of Statistics 2006, Vol. 34, No. 1, 373-393
 doi:10.1214/009053605000000741

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arXiv