A new nonparametric test for high-dimensional regression coefficients

Several tests for high-dimensional (large p, small n) regression coefficients have been proposed in the recent literature, but they are adversely affected by outlying observations and heavy-tailed distributions. In order to attack these challenges, a novel nonparametric testing procedure is developed under the framework of rank-based inference and is robust with respect to both the responses and the covariates. Besides, the proposed test statistic is invariant under the group of scalar transformations, which implies that our test statistic can integrate all the individual information in a relatively fair way. The newly defined test has many desirable general asymptotic properties, such as normality and consistency when (n, p) -> infinity. We assess the finite-sample performance of the proposed test by examining its size and power via Monte Carlo simulation, which demonstrates an improvement over the previous literature.