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...

In this work, we consider a multivariate regression model with one-sided errors. We assume for the function to lie in general Hölder class and estimate it via nonparametric local polynomial approach that consists of minimization integral approximation lying above data points. While consideration covariates offers an undeniable opportunity from application-oriented standpoint, requires new metho...