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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.

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Author:Gilles BlanchardGND, Sylvain Delattre, Etienne Roquain
ISSN:1350-7265 (print)
ISSN:1573-9759 (online)
Parent Title (English):Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability
Publisher:International Statistical Institute
Place of publication:Voorburg
Document Type:Article
Year of first Publication:2014
Year of Completion:2014
Release Date:2017/03/27
Tag:continuous testing; false discovery rate; multiple testing; positive correlation; step-up; stochastic process
First Page:304
Last Page:333
Funder: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