{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,10]],"date-time":"2026-10-10T00:49:07Z","timestamp":1791593347234,"version":"4.3.4"},"reference-count":28,"publisher":"Institute of Mathematical Statistics","issue":"none","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Statist."],"published-print":{"date-parts":[[2008,1,1]]},"abstract":"<jats:p>We investigate the performance of a family of multiple comparison procedures for strong control of the False Discovery Rate ($\\mathsf{FDR}$). The $\\mathsf{FDR}$ is the expected False Discovery Proportion ($\\mathsf{FDP}$), that is, the expected fraction of false rejections among all rejected hypotheses. A number of refinements to the original Benjamini-Hochberg procedure [1] have been proposed, to increase power by estimating the proportion of true null hypotheses, either implicitly, leading to one-stage adaptive procedures [4, 7] or explicitly, leading to two-stage adaptive (or plug-in) procedures [2, 21]. We use a variant of the stochastic process approach proposed by Genovese and Wasserman [11] to study the fluctuations of the $\\mathsf{FDP}$ achieved with each of these procedures around its expectation, for independent tested hypotheses. We introduce a framework for the derivation of generic Central Limit Theorems for the $\\mathsf{FDP}$ of these procedures, characterizing the associated regularity conditions, and comparing the asymptotic power of the various procedures. We interpret recently proposed one-stage adaptive procedures [4, 7] as fixed points in the iteration of well known two-stage adaptive procedures [2, 21].<\/jats:p>","DOI":"10.1214\/08-ejs207","type":"journal-article","created":{"date-parts":[[2008,11,20]],"date-time":"2008-11-20T08:36:01Z","timestamp":1227170161000},"page":"1065-1110","source":"Crossref","is-referenced-by-count":22,"title":["Asymptotic properties of false discovery rate controlling procedures under independence"],"prefix":"10.1214","volume":"2","author":[{"given":"Pierre","family":"Neuvial","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"3","doi-asserted-by":"publisher","unstructured":"[3] Benjamini, Y. and Yekutieli, D. (2001). The control of the false discovery rate in multiple testing under dependency., <i>Ann. Statist.<\/i> <b>29<\/b>, 4, 1165\u20131188.","DOI":"10.1214\/aos\/1013699998"},{"key":"1","doi-asserted-by":"publisher","unstructured":"[1] Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing., <i>J. R. Stat. Soc. Ser. B Stat. Methodol.<\/i> <b>57<\/b>, 1, 289\u2013300.","DOI":"10.1111\/j.2517-6161.1995.tb02031.x"},{"key":"2","doi-asserted-by":"publisher","unstructured":"[2] Benjamini, Y., Krieger, A. M., and Yekutieli, D. (2006). Adaptive linear step-up procedures that control the false discovery rate., <i>Biometrika<\/i> <b>93<\/b>, 3, 491\u2013507.","DOI":"10.1093\/biomet\/93.3.491"},{"key":"5","doi-asserted-by":"publisher","unstructured":"[5] Chi, Z. (2007). On the performance of FDR control: constraints and a partial solution., <i>Ann. Statist.<\/i> <b>35<\/b>, 4, 1409\u20131431.","DOI":"10.1214\/009053607000000037"},{"key":"6","unstructured":"[6] Donsker, M. D. (1951). An invariance principle for certain probability limit theorems., <i>Mem. Amer. Math. Soc.<\/i> <i>6<\/i>, 12."},{"key":"8","doi-asserted-by":"publisher","unstructured":"[8] Finner, H. and Roters, M. (2001). On the false discovery rate and expected type I errors., <i>Biom. J.<\/i> <b>43<\/b>, 8, 985\u20131005.","DOI":"10.1002\/1521-4036(200112)43:8<985::AID-BIMJ985>3.0.CO;2-4"},{"key":"9","doi-asserted-by":"publisher","unstructured":"[9] Finner, H. and Roters, M. (2002). Multiple hypotheses testing and expected number of type I errors., <i>Ann. Statist.<\/i> <b>30<\/b>, 1, 220\u2013238.","DOI":"10.1214\/aos\/1015362191"},{"key":"10","doi-asserted-by":"publisher","unstructured":"[10] Genovese, C. and Wasserman, L. (2002). Operating characteristics and extensions of the false discovery rate., <i>J. R. Stat. Soc. Ser. B Stat. Methodol.<\/i> <b>64<\/b>, 3, 499\u2013517.","DOI":"10.1111\/1467-9868.00347"},{"key":"11","doi-asserted-by":"publisher","unstructured":"[11] Genovese, C. and Wasserman, L. (2004). A stochastic process approach to false discovery control., <i>Ann. Statist.<\/i> <b>32<\/b>, 3, 1035\u20131061.","DOI":"10.1214\/009053604000000283"},{"key":"12","doi-asserted-by":"publisher","unstructured":"[12] Genovese, C. and Wasserman, L. (2006). Exceedance control of the false discovery proportion., <i>J. Amer. Statist. Assoc.<\/i> <b>101<\/b>, 476, 1408\u20131417.","DOI":"10.1198\/016214506000000339"},{"key":"13","doi-asserted-by":"publisher","unstructured":"[13] Lehmann, E. L. and Romano, J. P. (2005). Generalizations of the familywise error rate., <i>Ann. Statist<\/i> <b>33<\/b>, 3, 1138\u20131154.","DOI":"10.1214\/009053605000000084"},{"key":"15","doi-asserted-by":"publisher","unstructured":"[15] Perone Pacifico, M., Genovese, C., Verdinelli, I., and Wasserman, L. (2004). False discovery control for random fields., <i>J. Amer. Statist. Assoc.<\/i> <b>99<\/b>, 468, 1002\u20131014.","DOI":"10.1198\/0162145000001655"},{"key":"17","doi-asserted-by":"publisher","unstructured":"[17] Romano, J. P. and Shaikh, A. M. (2006b). Step-up procedures for control of generalizations of the family-wise error rate., <i>Ann. Statist.<\/i> <b>34<\/b>, 4, 1850\u20131873.","DOI":"10.1214\/009053606000000461"},{"key":"18","doi-asserted-by":"publisher","unstructured":"[18] Romano, J. P. and Wolf, M. (2007). Control of generalized error rates in multiple testing., <i>Ann. Statist.<\/i> <b>35<\/b>, 4, 1378\u20131408.","DOI":"10.1214\/009053606000001622"},{"key":"19","doi-asserted-by":"publisher","unstructured":"[19] Sarkar, S. K. (2002). Some results on false discovery rate in stepwise multiple testing procedures., <i>Ann. Statist.<\/i> <b>30<\/b>, 1, 239\u2013257.","DOI":"10.1214\/aos\/1015362192"},{"key":"20","doi-asserted-by":"publisher","unstructured":"[20] Simes, R. J. (1986). An improved Bonferroni procedure for multiple tests of significance., <i>Biometrika<\/i> <b>73<\/b>, 3, 751-754.","DOI":"10.1093\/biomet\/73.3.751"},{"key":"21","doi-asserted-by":"publisher","unstructured":"[21] Storey, J. D. (2002). A direct approach to false discovery rates., <i>J. R. Stat. Soc. Ser. B Stat. Methodol.<\/i> <b>64<\/b>, 3, 479\u2013498.","DOI":"10.1111\/1467-9868.00346"},{"key":"22","doi-asserted-by":"publisher","unstructured":"[22] Storey, J. D. (2003). The positive false discovery rate: a bayesian interpretation and the q-value., <i>Ann. Statist.<\/i> <b>31<\/b>, 6, 2013\u20132035.","DOI":"10.1214\/aos\/1074290335"},{"key":"23","doi-asserted-by":"publisher","unstructured":"[23] Storey, J. D., Taylor, J. E., and Siegmund, D. (2004). Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: a unified approach., <i>J. R. Stat. Soc. Ser. B Stat. Methodol.<\/i> <b>66<\/b>, 1, 187\u2013205.","DOI":"10.1111\/j.1467-9868.2004.00439.x"},{"key":"25","doi-asserted-by":"publisher","unstructured":"[25] Sun, W. and Cai, T. T. (2007). Oracle and adaptive compound decision rules for false discovery rate control., <i>J. Amer. Statist. Assoc.<\/i> <i>102<\/i>, 479, 901\u2013912.","DOI":"10.1198\/016214507000000545"},{"key":"26","doi-asserted-by":"crossref","unstructured":"[26] van der Laan, M. J., Dudoit, S., and Pollard, K. S. (2004). Augmentation procedures for control of the generalized family-wise error rate and tail probabilities for the proportion of false positives., <i>Stat. Appl. Genet. Mol. Biol.<\/i> <b>3<\/b>, Art. 15, 27 pp.","DOI":"10.2202\/1544-6115.1042"},{"key":"28","doi-asserted-by":"publisher","unstructured":"[28] Wu, W. B. (2008). On false discovery control under dependence., <i>Ann. Statist.<\/i> <b>36<\/b>, 1, 364\u2013380.","DOI":"10.1214\/009053607000000730"},{"key":"4","doi-asserted-by":"crossref","unstructured":"[4] Blanchard, G. and Roquain, E. (2008). Adaptive FDR control under independence and dependence. arXiv preprint, math.ST\/0707.0536v2.","DOI":"10.1214\/08-EJS180"},{"key":"7","doi-asserted-by":"publisher","unstructured":"[7] Finner, H., Dickhaus, T., and Roters, M. (2008). On the false discovery rate and an asymptotically optimal rejection curve., <i>Ann. Statist.<\/i> (to appear).","DOI":"10.1214\/07-AOS569"},{"key":"14","doi-asserted-by":"publisher","unstructured":"[14] Neuvial, P. (2008). Intrinsic bounds and false discovery rate control in multiple testing problems. In revision for, <i>J. Mach. Learn. Res.<\/i>","DOI":"10.1214\/08-EJS207"},{"key":"16","doi-asserted-by":"crossref","unstructured":"[16] Romano, J. P. and Shaikh, A. M. (2006a). On stepdown control of the false discovery proportion. In, <i>Optimality: The Second Erich L. Lehmann Symposium<\/i>, J. Rojo, Ed. Vol. <b>33<\/b>. Institute of Mathematical Statistics, Beachwood, Ohio, USA.","DOI":"10.1214\/074921706000000383"},{"key":"24","doi-asserted-by":"crossref","unstructured":"[24] Storey, J. D. and Tibshirani, R. (2003). SAM thresholding and false discovery rates for detecting differential gene expression in DNA microarrays. In, <i>The Analysis of Gene Expression Data: Methods and Software<\/i>. Springer, New York, 272\u2013290.","DOI":"10.1007\/0-387-21679-0_12"},{"key":"27","doi-asserted-by":"crossref","unstructured":"[27] van der Vaart, A. W. (1998)., <i>Asymptotic Statistics<\/i>. Cambridge University Press.","DOI":"10.1017\/CBO9780511802256"}],"container-title":["Electronic Journal of Statistics"],"original-title":[],"link":[{"URL":"https:\/\/projecteuclid.org\/download\/pdfview_1\/euclid.ejs\/1227287693","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T23:59:04Z","timestamp":1791590344000},"score":1,"resource":{"primary":{"URL":"https:\/\/projecteuclid.org\/journals\/electronic-journal-of-statistics\/volume-2\/issue-none\/Asymptotic-properties-of-false-discovery-rate-controlling-procedures-under-independence\/10.1214\/08-EJS207.full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1,1]]},"references-count":28,"journal-issue":{"issue":"none","published-online":{"date-parts":[[2008,1,1]]}},"URL":"https:\/\/doi.org\/10.1214\/08-ejs207","relation":{},"ISSN":["1935-7524","1935-7524"],"issn-type":[{"value":"1935-7524","type":"print"},{"value":"1935-7524","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1,1]]}}}