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

Sylvain Delattre (1) , Etienne Roquain (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

The false discovery proportion (FDP) is a convenient way to account for false positives when a large number of tests are performed simultaneously. Romano and Wolf (2007) 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 \cite{Korn2004,RW2007}. 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 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 non-asymptotically and asymptotically. Third, we introduce suitable modifications of this heuristic that provide new methods overcoming the existing procedures with a proven FDP control.

Domaines: Théorie [stat.TH]

Sylvain Delattre, Etienne Roquain. New procedures controlling the false discovery proportion via Romano-Wolf's heuristic. 2014. ⟨hal-00905060v3⟩