Adaptive FDR control under independence and dependence

By Gilles Blanchard, Étienne Roquain. 2007

53 citations recorded by the source corpus.

In the context of multiple hypotheses testing, the proportion $\pi_0$ of true null hypotheses in the pool of hypotheses to test often plays a crucial role, although it is generally unknown a priori. A testing procedure using an implicit or explicit estimate of this quantity in order to improve its efficency is called adaptive. In this paper, we focus on the issue of False Discovery Rate (FDR) control and we present new adaptive multiple testing procedures with control of the FDR. First, in the context of assuming independent $p$-values, we present two new procedures and give a unified review of other existing adaptive procedures that have provably controlled FDR. We report extensive simulation results comparing these procedures and testing their robustness when the independence assumption is violated. The new proposed procedures appear competitive with existing ones. The overall best, though, is reported to be Storey's estimator, but for a parameter setting that does not appear to have been considered before. Second, we propose adaptive versions of step-up procedures that have provably controlled FDR under positive dependences and unspecified dependences of the $p$-values, respectively. While simulations only show an improvement over non-adaptive procedures in limited situations, these are to our knowledge among the first theoretically founded adaptive multiple testing procedures that control the FDR when the $p$-values are not independent.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/297729649e7cc13fb54880ac4cf49ef89dfd72a7

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Citations in the corpus

Two simple sufficient conditions for FDR control (2008, methodology): “A more extensive treatment of the question of adaptive procedures when following the general principles exposed in the present work, including other applications of Lemma 4.3, is proposed by Blanchard and Roquain (2008a) (see also the second author’s PhD thesis, Roquain, 2007, Chap.”
Discovering the false discovery rate (2010, background): “Adjustments may be needed in the estimator: see Storey et al. (2004), Benjamini et al. (2006), Gavrilov et al. (2009) and Blanchard and Roquain (2009) for modifications introduced to natural estimators.”
Exact calculations for false discovery proportion with application to least favorable configurations (2010, methodology): “A simulation study was done in [5] in order to check if their respective FDR is still below α (or at least close to α) in the EMN model.”