Dependency and false discovery rate: Asymptotics

• 成果类型: Article
• 署名作者: Finner, Helmut; Dickhaus, Thorsten; Roters, Markus
• 署名单位: Leibniz Association; Deutsches Diabetes-Zentrum (DDZ); Heinrich Heine University Dusseldorf
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000046
• 发表日期: 2007
• 页码: 1432-1455
• 关键词: i errors; inequalities

摘要

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' 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.