{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-online-control-of-false-discovery-rate","title":"On Online Control of False Discovery Rate","arxiv_id":"1502.06197","date":"2015-02-22","proceeding":null,"authors":["Adel Javanmard","Andrea Montanari"],"abstract":"Multiple hypotheses testing is a core problem in statistical inference and\narises in almost every scientific field. Given a sequence of null hypotheses\n$\\mathcal{H}(n) = (H_1,..., H_n)$, Benjamini and Hochberg\n\\cite{benjamini1995controlling} introduced the false discovery rate (FDR)\ncriterion, which is the expected proportion of false positives among rejected\nnull hypotheses, and proposed a testing procedure that controls FDR below a\npre-assigned significance level. They also proposed a different criterion,\ncalled mFDR, which does not control a property of the realized set of tests;\nrather it controls the ratio of expected number of false discoveries to the\nexpected number of discoveries.\n  In this paper, we propose two procedures for multiple hypotheses testing that\nwe will call \"LOND\" and \"LORD\". These procedures control FDR and mFDR in an\n\\emph{online manner}. Concretely, we consider an ordered --possibly infinite--\nsequence of null hypotheses $\\mathcal{H} = (H_1,H_2,H_3,...)$ where, at each\nstep $i$, the statistician must decide whether to reject hypothesis $H_i$\nhaving access only to the previous decisions. To the best of our knowledge, our\nwork is the first that controls FDR in this setting. This model was introduced\nby Foster and Stine \\cite{alpha-investing} whose alpha-investing rule only\ncontrols mFDR in online manner.\n  In order to compare different procedures, we develop lower bounds on the\ntotal discovery rate under the mixture model and prove that both LOND and LORD\nhave nearly linear number of discoveries. We further propose adjustment to LOND\nto address arbitrary correlation among the $p$-values. Finally, we evaluate the\nperformance of our procedures on both synthetic and real data comparing them\nwith alpha-investing rule, Benjamin-Hochberg method and a Bonferroni procedure.","url_abs":"http://arxiv.org/abs/1502.06197v2","url_pdf":"http://arxiv.org/pdf/1502.06197v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"on-online-control-of-false-discovery-rate","repo_url":"https://github.com/dsrobertson/onlineFDR","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1502.06197","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}