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.

本研究针对有限数量的假设，研究了一种自适应的步下过程，该过程源于 BH 线性步上过程对误发现率的重复使用，并利用临界常数 iq/[(m+1-i (1-q)]，其中 i=1,...,m。在对独立检验统计量的 FDR 控制下，我们证明了该步下程序在水平 q 处控制了 FDR，与其他两种 FDR 控制已经在独立性方面得到证明的程序相比，我们在独立性和 FDR 控制方面进行了数值比较。