Nonparametric conditional mean testing via an extreme‐type statistic in high dimension

We propose a new test to investigate the conditional mean dependence between a response variable and the corresponding covariates in the high‐dimensional regimes. The test statistic is an extreme‐type one built on the nonparametric method. The limiting null distribution of the proposed extreme type statistic under a mild mixing condition is established. Moreover, to make the test more powerful in general structures we propose a more general test statistic and develop its asymptotic properties. The power analysis of both methods is also considered. In real data analysis, we also propose a new way to conduct the feature screening based on our results. To evaluate the performance of our estimators and other methods, extensive simulations are conducted.