RESIDUAL PERMUTATION TEST FOR REGRESSION COEFFICIENT TESTING

• 成果类型: Article
• 署名作者: Wen, Kaiyue; Wang, Tengyao; Wang, Yuhao
• 署名单位: Stanford University; University of London; London School Economics & Political Science; Tsinghua University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2479
• 发表日期: 2025
• 页码: 724-748
• 关键词: confidence-intervals; randomization tests; robust; bootstrap; inference; variance; symmetry; anova

摘要

We consider the problem of testing whether a single coefficient is equal to zero in linear models when the dimension of covariates p can be up to a constant fraction of sample size n. In this regime, an important topic is to propose tests with finite-sample valid size control without requiring the noise to follow strong distributional assumptions. In this paper, we propose a new method, called the residual permutation test (RPT), which is constructed by projecting the regression residuals onto the space orthogonal to the union of the column spaces of the original and permuted design matrices. RPT can be proved to achieve finite-sample size validity under fixed design with just exchangeable noises, whenever p < n/2. Moreover, RPT is shown to be asymptotically powerful for heavy-tailed noises with bounded (1 + t)th order moment when the true coefficient is at least of order n(-t/(1+t)) for t is an element of [0, 1]. We further proved that this signal size requirement is essentially rate-optimal in the minimax sense. Numerical studies confirm that RPT performs well in a wide range of simulation settings with normal and heavy-tailed noise distributions.