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It combines accumulation tests from ordered multiple testing with data-carving ideas from post-selection inference, allowing highly flexible adaptation to generic structural information. Our procedure defines an interactive protocol for gradually pruning a candidate rejection set, beginning with the set of all hypotheses and shrinking the set with each step. By restricting the information at each step via a technique we call masking, our protocol enables interaction while controlling the false discovery rate in finite samples for any data-adaptive update rule that the analyst may choose. We suggest update rules for a variety of applications with complex structural constraints, demonstrate that selectively traversed accumulation rules perform well in problems ranging from convex region detection to false discovery rate control on directed acyclic graphs, and show how to extend the framework to regression problems where knockoff statistics are available in lieu of $p$-values.<\/jats:p>","DOI":"10.1093\/biomet\/asaa064","type":"journal-article","created":{"date-parts":[[2020,7,24]],"date-time":"2020-07-24T11:25:03Z","timestamp":1595589903000},"page":"253-267","source":"Crossref","is-referenced-by-count":15,"title":["A general interactive framework for false discovery rate control under structural constraints"],"prefix":"10.1093","volume":"108","author":[{"given":"Lihua","family":"Lei","sequence":"first","affiliation":[{"name":"Department of Statistics, Stanford University, 202 Sequoia Hall, 390 Serra Mall, Stanford, California 94305, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aaditya","family":"Ramdas","sequence":"additional","affiliation":[{"name":"Department of Statistics and Data Science, Carnegie Mellon University, 132H Baker Hall, Pittsburgh, Pennsylvania 15213, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"William","family":"Fithian","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of California, Berkeley, 301 Evans Hall, Berkeley, California 94720, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,7,31]]},"reference":[{"key":"2021051519494335700_B1","doi-asserted-by":"crossref","first-page":"2055","DOI":"10.1214\/15-AOS1337","article-title":"Controlling the false discovery rate via knockoffs","volume":"43","author":"Barber,","year":"2015","journal-title":"Ann. 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