While multivariate statistical inference procedures are commonly available for low dimensional-data, such procedures are not applicable for high dimensional data where the number of variables (dimension) is larger than the sample size unless extensions/modifications are done. A new test is proposed for the overall significance of coefficients in high-dimensional linear regression models based on estimated U-statistics of order two and refitted cross-validation error variance estimation. The model settings and the proposed new test for the significance of high-dimensional regression coefficients are introduced. The asymptotic distributions of the test statistics are derived under the null hypothesis or the local alternatives. Monte Carlo simulations are conducted and the empirical results presented. The proposed method is demonstrated using an application by an empirical analysis of a microarray data set.
展开▼
