On the false discovery rate and an asymptotically optimal rejection curve

By Helmut Finner, Thorsten Dickhaus, Markus Roters. 2009

122 citations recorded by the source corpus.

In this paper we introduce and investigate a new rejection curve for asymptotic control of the false discovery rate (FDR) in multiple hypotheses testing problems. We first give a heuristic motivation for this new curve and propose some procedures related to it. Then we introduce a set of possible assumptions and give a unifying short proof of FDR control for procedures based on Simes' critical values, whereby certain types of dependency are allowed. This methodology of proof is then applied to other fixed rejection curves including the proposed new curve. Among others, we investigate the problem of finding least favorable parameter configurations such that the FDR becomes largest. We then derive a series of results concerning asymptotic FDR control for procedures based on the new curve and discuss several example procedures in more detail. A main result will be an asymptotic optimality statement for various procedures based on the new curve in the class of fixed rejection curves. Finally, we briefly discuss strict FDR control for a finite number of hypotheses.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1c49766cd3d2e19089fea703e579a73011946ac7

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Two simple sufficient conditions for FDR control (2008, methodology): “…e Because this function is now data-dependent, establishing FDR control for the resulting procedure is more delicate; it is the subject of numerous recent works (see, e.g., Black, 2004; Benjamini et al., 2006; Finner et al., 2008; see also Gavrilov et al., 2008 for an adaptive step-down procedure).”
Multiple hypothesis testing in genomics (2014, methodology): “For the Benjamini & Hochberg procedure, the ‘worst case’ for which the procedure is least conservative is the dirac-uniform configuration in which all false hypotheses always have p-values exactly zero, and p-values of true null hypotheses are independent and uniform [25].”
Exact calculations for false discovery proportion with application to least favorable configurations (2010, methodology): “Considering step-up or step-down methods requires more eﬀorts: when the p -values are all i.i.d. uniform, the exact distribution of the rejection number has been computed by Finner and Roters (2002) for step-up and step-down procedures, which leads to a computation of the FDR in the degenerate case ”
Adaptive FDR control under independence and dependence (2007, background): “In addition, some other works (Genovese and Wasserman, 2004; Storey et al., 2004; Finner et al., 2009) have studied the question of adaptivity to the parameter π0 from an asymptotic viewpoint.”
An adaptive step-down procedure with proven FDR control under independence (2009, methodology): “Independently, within the same asymptotic framework of a mixture model, Finner, Dickhaus and Roters [7] were interested in the form of an asymptotically optimal curve to which the empirical distribution of the p-values”
The Bayes oracle and asymptotic optimality of multiple testing procedures under sparsity (2010, methodology): “In [20] an asymptotic analysis is performed and new step-up and step-up-down procedures, which maximize the asymptotic power while controlling the asymptotic FDR, are introduced.”
Optimal weighting for false discovery rate control (2008, methodology): “Only few works have studied rigorously the optimality of certain classes of multiple testing procedures (see Lehmann et al. (2005); Wasserman and Roeder (2006); Rubin et al. (2006); Storey (2007); Finner et al. (2009)).”