NEW PROCEDURES CONTROLLING THE FALSE DISCOVERY PROPORTION VIA ROMANO-WOLF'S HEURISTIC

• 成果类型: Article
• 署名作者: Delattre, Sylvain; Roquain, Etienne
• 署名单位: Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1302
• 发表日期: 2015
• 页码: 1141-1177
• 关键词: familywise error rate; central-limit-theorem; FDR CONTROL; stepup procedures; moment bounds; dependence; INDEPENDENCE; inequalities; exceedance; rates

摘要

The false discovery proportion (FDP) is a convenient way to account for false positives when a large number m of tests are performed simultaneously. Romano and Wolf [Ann. Statist. 35 (2007) 1378-1408] have proposed a general principle that builds FDP controlling procedures from k-family-wise error rate controlling procedures while incorporating dependencies in an appropriate manner; see Korn et al. [J. Statist. Plann. Inference 124 (2004) 379-398]; Romano and Wolf (2007). However, the theoretical validity of the latter is still largely unknown. This paper provides a careful study of this heuristic: first, we extend this approach by using a notion of bounding device that allows us to cover a wide range of critical values, including those that adapt to m(0), the number of true null hypotheses. Second, the theoretical validity of the latter is investigated both nonasymptotically and asymptotically. Third, we introduce suitable modifications of this heuristic that provide new methods, overcoming the existing procedures with a proven FDP control.