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Under the assumption of an Archimedean $p$-value copula with completely monotone generator, we derive a sharper upper bound for the FDR of $\\varphi^{LSU}$ as well as a non-trivial lower bound. Application of the sharper upper bound to parametric subclasses of Archimedean $p$-value copulae allows us to increase the power of $\\varphi^{LSU}$ by pre-estimating the copula parameter and adjusting $q$. Based on the lower bound, a sufficient condition is obtained under which the FDR of $\\varphi^{LSU}$ is exactly equal to $m_{0}q\/m$, as in the case of stochastically independent $p$-values. Finally, we deal with high-dimensional multiple test problems with exchangeable test statistics by drawing a connection between infinite sequences of exchangeable $p$-values and Archimedean copulae with completely monotone generators. Our theoretical results are applied to important copula families, including Clayton copulae and Gumbel-Hougaard copulae.<\/jats:p>","DOI":"10.1214\/14-ejs950","type":"journal-article","created":{"date-parts":[[2014,10,29]],"date-time":"2014-10-29T09:09:35Z","timestamp":1414573775000},"page":"2207-2241","source":"Crossref","is-referenced-by-count":11,"title":["False discovery rate control under Archimedean copula"],"prefix":"10.1214","volume":"8","author":[{"given":"Taras","family":"Bodnar","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thorsten","family":"Dickhaus","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"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. 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