Mathematics – Statistics Theory
Scientific paper
2005-01-19
Annals of Statistics 2006, Vol. 34, No. 1, 373-393
Mathematics
Statistics Theory
Published at http://dx.doi.org/10.1214/009053605000000741 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst
Scientific paper
10.1214/009053605000000741
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 $100(1-\alpha)%$ 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 $\alpha \to 0$ as the number of hypothesis tests increases and the proportion decreases. This work is motivated by a signal detection problem that occurs in astronomy.
Meinshausen Nicolai
Rice Jr. J.
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