High-dimensional analysis of variance in multivariate linear regression
本文针对多元线性回归中系数维度和样本量同步增长的高维场景，提出一种新的U型统计量来检验线性假设，并在较弱的矩条件下建立了高维高斯逼近理论，可用于经典和单因素非参数多元方差分析。
Summary 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.