2023/01/10 by Zhipeng Lou, Xianyang Zhang, Lou, Zhipeng +3
Computer Science · Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Face and Expression Recognition #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2301.04209
openalex publication_date 2023/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 test 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 applied to deal with the classical one-way multivariate ANOVA and the nonparametric one-way MANOVA in high dimensions. To implement the test procedure in practice, 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.