Two-stage stepup procedures controlling FDR

A two-stage stepup procedure is defined and an explicit formula for the FDR of this procedure is derived under any distributional setting. Sets of critical values are determined that provide a control of the FDR of a two-stage stepup procedure under iid mixture model. A class of two-stage FDR procedures modifying the Benjamini–Hochberg (BH) procedure and containing the one given in Storey et al. [2004. Strong control, conservative point estimation and simultanaeous conservative consistency of false discovery rates: a unified approach. J. Roy. Statist. Soc. Ser. B 66, 187–205] is obtained. The FDR controlling property of the Storey–Taylor–Siegmund procedure is proved only under the independence, which is different from that presented by these authors. A single-stage stepup procedure controlling the FDR under any form of dependence, which is different from and in some situations performs better than the Benjamini–Yekutieli (BY) procedure, is given before discussing how to obtain two-stage versions of the BY and this new procedures. Simulations reveal that procedures proposed in this article under the mixture model can perform quite well in terms of improving the FDR control of the BH procedure. However, the similar idea of improving the FDR control of a stepup procedure under any form dependence does not seem to work.