文章基本信息

标题：Coarse-to-fine multiple testing strategies
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作者：Kamel Lahouel ; Donald Geman ; Laurent Younes 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2019
卷号：13
期号：1
页码：1292-1328
DOI：10.1214/19-EJS1536
语种：English
出版社：Institute of Mathematical Statistics
摘要：We analyze control of the familywise error rate (FWER) in a multiple testing scenario with a great many null hypotheses about the distribution of a high-dimensional random variable among which only a very small fraction are false, or “active”. In order to improve power relative to conservative Bonferroni bounds, we explore a coarse-to-fine procedure adapted to a situation in which tests are partitioned into subsets, or “cells”, and active hypotheses tend to cluster within cells. We develop procedures for a non-parametric case based on generalized permutation testing and a linear Gaussian model, and demonstrate higher power than Bonferroni estimates at the same FWER when the active hypotheses do cluster. The main technical difficulty arises from the correlation between the test statistics at the individual and cell levels, which increases the likelihood of a hypothesis being falsely discovered when the cell that contains it is falsely discovered (survivorship bias). This requires sharp estimates of certain quadrant probabilities when a cell is inactive.