CONSISTENCY OF INVARIANCE-BASED RANDOMIZATION TESTS

• 成果类型: Article
• 署名作者: Dobriban, Edgar
• 署名单位: University of Pennsylvania
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/22-AOS2200
• 发表日期: 2022
• 页码: 2443-2466
• 关键词: asymptotic expansions; permutation methods; POWER; hypotheses; expression; suprema; set

摘要

Invariance-based randomization tests-such as permutation tests, rotation tests, or sign changes-are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data distribution. Most work focuses on their type I error control properties, while their consistency properties are much less understood. We develop a general framework to study the consistency of invariance-based randomization tests, assuming the data is drawn from a signal-plusnoise model. We allow the transforms (e.g., permutations or rotations) to be general compact topological groups, such as rotation groups, acting by linear group representations. We study test statistics with a generalized subadditivity property. We apply our framework to a number of fundamental and highly important problems in statistics, including sparse vector detection, testing for low-rank matrices in noise, sparse detection in linear regression, and two-sample testing. Comparing with minimax lower bounds we develop, we find perhaps surprisingly that in some cases, randomization tests detect signals at the minimax optimal rate.