The Annals of Statistics
- Ann. Statist.
- Volume 34, Number 1 (2006), 373-393.
Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses
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→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.
Ann. Statist. Volume 34, Number 1 (2006), 373-393.
First available in Project Euclid: 2 May 2006
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Meinshausen, Nicolai; Rice, John. Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses. Ann. Statist. 34 (2006), no. 1, 373--393. doi:10.1214/009053605000000741. http://projecteuclid.org/euclid.aos/1146576267.