The Annals of Statistics

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

Yulia Gavrilov, Yoav Benjamini, and Sanat K. Sarkar

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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.

Article information

Ann. Statist., Volume 37, Number 2 (2009), 619-629.

First available in Project Euclid: 10 March 2009

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Zentralblatt MATH identifier

Primary: 62J15: Paired and multiple comparisons

Multiple testing false discovery rate


Gavrilov, Yulia; Benjamini, Yoav; Sarkar, Sanat K. An adaptive step-down procedure with proven FDR control under independence. Ann. Statist. 37 (2009), no. 2, 619--629. doi:10.1214/07-AOS586.

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