Stepdown Procedures Controlling A Generalized False Discovery Rate

Often in practice when a large number of hypotheses are simultaneously tested, one is willing to allow a few false rejections, say at most k−1, for some fixed k > 1. In such a case, the ability of a procedure controlling an error rate measuring at least one false rejection can potentially be improved in terms of its ability to detect false null hypotheses by generalizing this error rate to one that measures at least k false rejections and using procedures that control it. The k-FDR which is the expected proportion of k or more false rejections and a natural generalization of the false discovery rate (FDR) is such a generalized notion of error rate that has recently been introduced and procedures controlling it have been proposed. Many of these procedures are stepup procedures. Some stepdown procedures controlling the k-FDR are presented in this article.