{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,10]],"date-time":"2026-10-10T00:50:47Z","timestamp":1791593447610,"version":"4.3.4"},"reference-count":16,"publisher":"Institute of Mathematical Statistics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann. Statist."],"published-print":{"date-parts":[[2007,8,1]]},"abstract":"<jats:p>Some effort has been undertaken over the last decade to provide conditions for the control of the false discovery rate by the linear step-up procedure (LSU) for testing $n$ hypotheses when test statistics are dependent. In this paper we investigate the expected error rate (EER) and the false discovery rate (FDR) in some extreme parameter configurations when $n$ tends to infinity for test statistics being exchangeable under null hypotheses. All results are derived in terms of $p$-values. In a general setup we present a series of results concerning the interrelation of Simes\u2019 rejection curve and the (limiting) empirical distribution function of the $p$-values. Main objects under investigation are largest (limiting) crossing points between these functions, which play a key role in deriving explicit formulas for EER and FDR. As specific examples we investigate equi-correlated normal and $t$-variables in more detail and compute the limiting EER and FDR theoretically and numerically. A surprising limit behavior occurs if these models tend to independence.<\/jats:p>","DOI":"10.1214\/009053607000000046","type":"journal-article","created":{"date-parts":[[2007,10,3]],"date-time":"2007-10-03T11:18:56Z","timestamp":1191410336000},"page":"1432-1455","source":"Crossref","is-referenced-by-count":57,"title":["Dependency and false discovery rate: Asymptotics"],"prefix":"10.1214","volume":"35","author":[{"given":"Helmut","family":"Finner","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thorsten","family":"Dickhaus","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Markus","family":"Roters","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"2","doi-asserted-by":"publisher","unstructured":"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> 1165\u20131188.","DOI":"10.1214\/aos\/1013699998"},{"key":"8","doi-asserted-by":"publisher","unstructured":"Finner, H. and Roters, M. (2002). Multiple hypotheses testing and expected number of type I errors. <i>Ann. Statist.<\/i> <b>30<\/b> 220\u2013238.","DOI":"10.1214\/aos\/1015362191"},{"key":"10","doi-asserted-by":"publisher","unstructured":"Genovese, C. R. and Wasserman, L. (2004). A stochastic process approach to false discovery control. <i>Ann. Statist.<\/i> <b>32<\/b> 1035\u20131061.","DOI":"10.1214\/009053604000000283"},{"key":"16","doi-asserted-by":"publisher","unstructured":"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> 187\u2013205.","DOI":"10.1111\/j.1467-9868.2004.00439.x"},{"key":"13","doi-asserted-by":"publisher","unstructured":"Sarkar, S. K. (2002). Some results on false discovery rate in stepwise multiple testing procedures. <i>Ann. Statist.<\/i> <b>30<\/b> 239\u2013257.","DOI":"10.1214\/aos\/1015362192"},{"key":"5","doi-asserted-by":"publisher","unstructured":"Finner, H. and Roters, M. (1998). Asymptotic comparison of step-down and step-up multiple test procedures based on exchangeable test statistics. <i>Ann. Statist.<\/i> <b>26<\/b> 505\u2013524.","DOI":"10.1214\/aos\/1028144847"},{"key":"11","unstructured":"Karlin, S. (1968). <i>Total Positivity<\/i> <b>1<\/b>. Stanford Univ. Press."},{"key":"15","doi-asserted-by":"publisher","unstructured":"Simes, R. J. (1986). An improved Bonferroni procedure for multiple tests of significance. <i>Biometrika<\/i> <b>73<\/b> 751\u2013754.","DOI":"10.1093\/biomet\/73.3.751"},{"key":"1","doi-asserted-by":"publisher","unstructured":"Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. <i>J. Roy. Statist. Soc. Ser. B <\/i> <b>57<\/b> 289\u2013300.","DOI":"10.1111\/j.2517-6161.1995.tb02031.x"},{"key":"3","unstructured":"Eklund, G. and Seeger, P. (1965). Massignifikansanalys. <i> Statistisk Tidskrift Stockholm<\/i> <b>3<\/b> 355\u2013365."},{"key":"4","doi-asserted-by":"publisher","unstructured":"Finner, H., Dickhaus, T. and Roters, M. (2008). Asymptotic tail properties of Student's $t$-distribution. <i>Comm. Statist. Theory Methods<\/i> <b>37<\/b>. To appear.","DOI":"10.1080\/03610920701649019"},{"key":"6","doi-asserted-by":"publisher","unstructured":"Finner, H. and Roters, M. (2001). Asymptotic sharpness of product-type inequalities for maxima of random variables with applications in multiple comparisons. <i>J. Statist. Plann. Inference<\/i> <b>98<\/b> 39\u201356.","DOI":"10.1016\/S0378-3758(00)00304-9"},{"key":"7","doi-asserted-by":"publisher","unstructured":"Finner, H. and Roters, M. (2001). On the false discovery rate and expected number of type I errors. <i>Biom. J.<\/i> <b>43<\/b> 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":"Genovese, C. R. and Wasserman, L. (2002). Operating characteristics and extensions of the false discovery rate procedure. <i>J. R. Stat. Soc. Ser. B Stat. Methodol.<\/i> <b>64<\/b> 499\u2013517.","DOI":"10.1111\/1467-9868.00347"},{"key":"12","doi-asserted-by":"publisher","unstructured":"Karlin, S. and Rinott, Y. (1980). Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions. <i>J. 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