An adaptive step-down procedure with proven FDR control under independence

By Yulia Gavrilov, Yoav Benjamini, Sanat K. Sarkar. 2009

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In this work we study an adaptive step-down procedure for testing m hypotheses. It stems from the repeated use of the false discovery rate controlling the linear step-up procedure (sometimes called BH), and makes use of the critical constants iq/[(m + 1 - i(1 - q)], i = 1,..., m. Motivated by its success as a model selection procedure, as well as by its asymptotic optimality, we are interested in its false discovery rate (FDR) controlling properties for a finite number of hypotheses. We prove this step-down procedure controls the FDR at level q for independent test statistics. We then numerically compare it with two other procedures with proven FDR control under independence, both in terms of power under independence and FDR control under positive dependence.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a97e8af759381536766a5c2dfcb611fa0066c93c

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In Management Science and Operations Research

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Citations in the corpus

Adaptive FDR control under independence and dependence (2007, methodology): “Finally, the step-down procedure based on the same threshold collection t(i) (without modification) is proposed and studied by Gavrilov et al. (2009). Using specific properties of step-down procedures, these authors proved the nonasymptotic FDR control of this procedure.”
A unified treatment of multiple testing with prior knowledge using the p-filter (2017, background): “[15] extending them to adaptive control under independence.”
Private False Discovery Rate Control (2015, background): “However, as shown in [13], the step-down BHq can assume less stringent critical values than the BHq critical values while still controls FDR, often allowing more discoveries than the step-up BHq.”
Exact calculations for false discovery proportion with application to least favorable configurations (2010, methodology): “As a consequence, Theorem 4.1 states that the LFC for the procedure of Gavrilov et al. (2009) is still the Dirac-uniform conﬁguration (over the class of concave c.d.f.’s), at least for the previously listed values of ( α, m ), which is a new interesting ﬁnding.”
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).”
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.”
Hypothesis Testing in Econometrics (2010, background): “The literature in this field is quite extensive and we refer the reader to Storey et al. (2004), Benjamini et al. (2006), Gavrilov et al. (2009), and the references therein.”
Optimal weighting for false discovery rate control (2008, methodology): “This result has been implicitly proved in Gavrilov et al. (2009) (Section 3), using a speciﬁc non-weighted step-down procedure.”