{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,10]],"date-time":"2026-10-10T06:42:00Z","timestamp":1791614520905,"version":"4.3.4"},"reference-count":17,"publisher":"Bernoulli Society for Mathematical Statistics and Probability","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bernoulli"],"published-print":{"date-parts":[[2014,2,1]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3150\/12-bej488","type":"journal-article","created":{"date-parts":[[2014,1,22]],"date-time":"2014-01-22T11:14:45Z","timestamp":1390389285000},"page":"304-333","source":"Crossref","is-referenced-by-count":10,"title":["Testing over a continuum of null hypotheses with False Discovery Rate control"],"prefix":"10.3150","volume":"20","author":[{"given":"Gilles","family":"Blanchard","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sylvain","family":"Delattre","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Etienne","family":"Roquain","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1726","reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"[1] Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. <i>J. Roy. Statist. Soc. Ser. B<\/i> <b>57<\/b> 289\u2013300.","DOI":"10.1111\/j.2517-6161.1995.tb02031.x"},{"key":"3","doi-asserted-by":"publisher","unstructured":"[3] Benjamini, Y. and Yekutieli, D. (2001). The control of the false discovery rate in multiple testing under dependency. <i>Ann. Statist.<\/i> <b>29<\/b> 1165\u20131188.","DOI":"10.1214\/aos\/1013699998"},{"key":"2","doi-asserted-by":"crossref","unstructured":"[2] Benjamini, Y. and Hochberg, Y. (1997). Multiple hypotheses testing with weights. <i>Scand. J. Stat.<\/i> <b>24<\/b> 407\u2013418.","DOI":"10.1111\/1467-9469.00072"},{"key":"5","doi-asserted-by":"crossref","unstructured":"[5] Blanchard, G., Delattre, S. and Roquain, E. (2014). 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New York: Wiley.","DOI":"10.1002\/9780470316962"}],"container-title":["Bernoulli"],"original-title":[],"deposited":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T17:22:41Z","timestamp":1791566561000},"score":1,"resource":{"primary":{"URL":"https:\/\/projecteuclid.org\/journals\/bernoulli\/volume-20\/issue-1\/Testing-over-a-continuum-of-null-hypotheses-with-False-Discovery\/10.3150\/12-BEJ488.full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,2,1]]},"references-count":17,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2014,2,1]]}},"URL":"https:\/\/doi.org\/10.3150\/12-bej488","relation":{},"ISSN":["1350-7265"],"issn-type":[{"value":"1350-7265","type":"print"}],"subject":[],"published":{"date-parts":[[2014,2,1]]}}}