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February 2006 Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses
Nicolai Meinshausen, John Rice
Ann. Statist. 34(1): 373-393 (February 2006). DOI: 10.1214/009053605000000741

Abstract

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.

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Nicolai Meinshausen. John Rice. "Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses." Ann. Statist. 34 (1) 373 - 393, February 2006. https://doi.org/10.1214/009053605000000741

Information

Published: February 2006
First available in Project Euclid: 2 May 2006

zbMATH: 1091.62059
MathSciNet: MR2275246
Digital Object Identifier: 10.1214/009053605000000741

Subjects:
Primary: 62H15
Secondary: 62J15 , 62P35

Keywords: Hypothesis testing , Multiple comparisons , Sparsity

Rights: Copyright © 2006 Institute of Mathematical Statistics

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Vol.34 • No. 1 • February 2006
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