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

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

2009-03-31

arxiv.org/abs/0903.5373v1

Annals of Statistics 2009, Vol. 37, No. 2, 619-629

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-AOS586 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/07-AOS586

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.

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