High-dimensional analysis of variance in multivariate linear regression

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