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.
@article{1146576267,
author = {Meinshausen, Nicolai and Rice, John},
title = {Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses},
journal = {Ann. Statist.},
volume = {34},
number = {1},
year = {2006},
pages = { 373-393},
language = {en},
url = {http://dml.mathdoc.fr/item/1146576267}
}
Meinshausen, Nicolai; Rice, John. Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses. Ann. Statist., Tome 34 (2006) no. 1, pp. 373-393. http://gdmltest.u-ga.fr/item/1146576267/