High-dimensional analysis of variance in multivariate linear regression

• 成果类型: Article
• 署名作者: Lou, Zhipeng; Zhang, Xianyang; Wu, Wei Biao
• 署名单位: Princeton University; Texas A&M University System; Texas A&M University College Station; University of Chicago
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asad001
• 发表日期: 2023
• 页码: 777797
• 关键词: asymptotic-distribution; resampling methods; robust regression; mean vectors; M-ESTIMATORS; statistics; dependence; jackknife; bootstrap; tests

摘要

In this paper, we develop a systematic theory for high-dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new U-type statistic to test linear hypotheses and establish a high-dimensional Gaussian approximation result under fairly mild moment assumptions. Our general framework and theory can be used to deal with the classical one-way multivariate analysis of variance, and the nonparametric one-way multivariate analysis of variance in high dimensions. To implement the test procedure, we introduce a sample-splitting-based estimator of the second moment of the error covariance and discuss its properties. A simulation study shows that our proposed test outperforms some existing tests in various settings.