SEQUENTIAL MULTIPLE TESTING WITH GENERALIZED ERROR CONTROL: AN ASYMPTOTIC OPTIMALITY THEORY

• 成果类型: Article
• 署名作者: Song, Yanglei; Fellouris, Georgios
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1737
• 发表日期: 2019
• 页码: 1776-1803
• 关键词: false discovery rate; family-wise error; rates

摘要

The sequential multiple testing problem is considered under two generalized error metrics. Under the first one, the probability of at least k mistakes, of any kind, is controlled. Under the second, the probabilities of at least k(1) false positives and at least k(2) false negatives are simultaneously controlled. For each formulation, the optimal expected sample size is characterized, to a first-order asymptotic approximation as the error probabilities go to 0, and a novel multiple testing procedure is proposed and shown to be asymptotically efficient under every signal configuration. These results are established when the data streams for the various hypotheses are independent and each local log-likelihood ratio statistic satisfies a certain strong law of large numbers. In the special case of i.i.d. observations in each stream, the gains of the proposed sequential procedures over fixed-sample size schemes are quantified.