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Many standard multiple testing procedures are self-consistent (e.g. step-up, step-down or step-up-down procedures), and we prove that the dependency control condition can be fulfilled when choosing correspondingly appropriate rejection functions, in three classical types of dependency: independence, positive dependency (PRDS) and unspecified dependency. As a consequence, we recover earlier results through simple and unifying proofs while extending their scope to several regards: weighted FDR, p-value reweighting, new family of step-up procedures under unspecified p-value dependency and adaptive step-up procedures. We give additional examples of other possible applications. This framework also allows for defining and studying FDR control for multiple testing procedures over a continuous, uncountable space of hypotheses.<\/jats:p>","DOI":"10.1214\/08-ejs180","type":"journal-article","created":{"date-parts":[[2008,10,15]],"date-time":"2008-10-15T09:05:57Z","timestamp":1224061557000},"page":"963-992","source":"Crossref","is-referenced-by-count":76,"title":["Two simple sufficient conditions for FDR control"],"prefix":"10.1214","volume":"2","author":[{"given":"Gilles","family":"Blanchard","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Etienne","family":"Roquain","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"16","unstructured":"Holm, S. (1979). A simple sequentially rejective multiple test procedure., <i>Scand. J. 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