FURTHER RESULTS ON CONTROLLING THE FALSE DISCOVERY PROPORTION

• 成果类型: Article
• 署名作者: Guo, Wenge; He, Li; Sarkar, Sanat K.
• 署名单位: New Jersey Institute of Technology; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1214
• 发表日期: 2014
• 页码: 1070-1101
• 关键词: stepup procedures; number; inequalities; dependence

摘要

The probability of false discovery proportion (FDP) exceeding gamma is an element of [0, 1), defined as gamma-FDP, has received much attention as a measure of false discoveries in multiple testing. Although this measure has received acceptance due to its relevance under dependency, not much progress has been made yet advancing its theory under such dependency in a nonasymptotic setting, which motivates our research in this article. We provide a larger class of procedures containing the stepup analog of, and hence more powerful than, the stepdown procedure in Lehmann and Romano [Ann. Statist. 33 (2005) 1138-1154] controlling the gamma-FDP under similar positive dependence condition assumed in that paper. We offer better alternatives of the stepdown and stepup procedures in Romano and Shaikh [IMS Lecture Notes Monogr: Ser. 49 (2006a) 33-50, Ann. Statist. 34 (2006b) 1850-1873] using pairwise joint distributions of the null p-values. We generalize the notion of gamma-FDP making it appropriate in situations where one is willing to tolerate a few false rejections or, due to high dependency, some false rejections are inevitable, and provide methods that control this generalized gamma-FDP in two different scenarios: (i) only the marginal p-values are available and (ii) the marginal p-values as well as the common pairwise joint distributions of the null p-values are available, and assuming both positive dependence and arbitrary dependence conditions on the p-values in each scenario. Our theoretical findings are being supported through numerical studies.