Fast closed testing for exchangeable local tests

• 成果类型: Article
• 署名作者: Dobriban, E.
• 署名单位: University of Pennsylvania
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asz082
• 发表日期: 2020
• 页码: 761768
• 关键词: rejective multiple test; BONFERRONI PROCEDURE; POWER

摘要

Multiple hypothesis testing problems arise naturally in science. This note introduces a new fast closed testing method for multiple testing which controls the familywise error rate. Controlling the familywise error rate is state-of-the-art in many important application areas and is preferred over false discovery rate control for many reasons, including that it leads to stronger reproducibility. The closure principle rejects an individual hypothesis if all global nulls of subsets containing it are rejected using some test statistics. It takes exponential time in the worst case. When the tests are symmetric and monotone, the proposed method is an exact algorithm for computing the closure, is quadratic in the number of tests, and is linear in the number of discoveries. Our framework generalizes most examples of closed testing, such as Holm's method and the Bonferroni method. As a special case of the method, we propose the Simes and higher criticism fusion test, which is powerful both for detecting a few strong signals and for detecting many moderate signals.