New procedures controlling the false discovery proportion via Romano-Wolf's heuristic

Abstract : The false discovery proportion (FDP) is a convenient way to account for false positives when a large number $m$ of tests are performed simultaneously. Romano and Wolf [Ann. Statist. 35 (2007) 1378-1408] have proposed a general principle that builds FDP controlling procedures from $k$-family-wise error rate controlling procedures while incorporating dependencies in an appropriate manner; see Korn et al. [J. Statist. Plann. Inference 124 (2004) 379-398]; Romano and Wolf (2007). However, the theoretical validity of the latter is still largely unknown. This paper provides a careful study of this heuristic: first, we extend this approach by using a notion of ``bounding device'' that allows us to cover a wide range of critical values, including those that adapt to $m_0$, the number of true null hypotheses. Second, the theoretical validity of the latter is investigated both nonasymptotically and asymptotically. Third, we introduce suitable modifications of this heuristic that provide A new methods, overcoming the existing procedures with a proven FDP control.
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Annals of Statistics, Institute of Mathematical Statistics, 2015, 43 (3), pp.1141-1177. <10.1214/14-AOS1302>
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Sylvain Delattre, Etienne Roquain. New procedures controlling the false discovery proportion via Romano-Wolf's heuristic. Annals of Statistics, Institute of Mathematical Statistics, 2015, 43 (3), pp.1141-1177. <10.1214/14-AOS1302>. <hal-00905060v4>

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