High-dimensional analysis of variance in multivariate linear regression

Zhipeng Lou, Xianyang Zhang and Wei Biao Wu

Biometrika, 2023, vol. 110, issue 3, 777-797

Abstract: SummaryIn 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.

Keywords: Data-splitting, Gaussian approximation, Multivariate analysis of variance, One-way layout; U statistic (search for similar items in EconPapers)
Date: 2023
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