Testing over a continuum of null hypotheses with False Discovery Rate control
- We consider statistical hypothesis testing simultaneously over a fairly general, possibly uncountably infinite, set of null hypotheses, under the assumption that a suitable single test (and corresponding p-value) is known for each individual hypothesis. We extend to this setting the notion of false discovery rate (FDR) as a measure of type I error. Our main result studies specific procedures based on the observation of the p-value process. Control of the FDR at a nominal level is ensured either under arbitrary dependence of p-values, or under the assumption that the finite dimensional distributions of the p-value process have positive correlations of a specific type (weak PRDS). Both cases generalize existing results established in the finite setting. Its interest is demonstrated in several non-parametric examples: testing the mean/signal in a Gaussian white noise model, testing the intensity of a Poisson process and testing the c.d.f. of i.i.d. random variables.
Author details: | Gilles BlanchardGND, Sylvain Delattre, Etienne Roquain |
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DOI: | https://doi.org/10.3150/12-BEJ488 |
ISSN: | 1350-7265 |
ISSN: | 1573-9759 |
Title of parent work (English): | Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability |
Publisher: | International Statistical Institute |
Place of publishing: | Voorburg |
Publication type: | Article |
Language: | English |
Year of first publication: | 2014 |
Publication year: | 2014 |
Release date: | 2017/03/27 |
Tag: | continuous testing; false discovery rate; multiple testing; positive correlation; step-up; stochastic process |
Volume: | 20 |
Issue: | 1 |
Number of pages: | 30 |
First page: | 304 |
Last Page: | 333 |
Funding institution: | IST Programme of the European Community, under the PASCAL Network of Excellence [IST-2002-506778]; French Agence Nationale de la Recherche (ANR ) [ANR-09-JCJC-0027-01]; French Agence Nationale de la Recherche (ANR-PARCIMONIE) [ANR-09-JCJC-0101-01]; French ministry of foreign and european affairs (EGIDE - PROCOPE) [21887] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |