We consider testing the significance of a subset of covariates in a nonparamet- ric regression. These covariates can be continuous and/or discrete. We propose a new kernel-based test that smoothes only over the covariates appearing under the null hypothesis, so that the curse of dimensionality is mitigated. The test statistic is asymptotically pivotal and the rate of which the test detects local alternatives depends only on the dimension of the covariates under the null hy- pothesis. We show the validity of wild bootstrap for the test. In small samples, our test is competitive compared to existing procedures.
Testing; Bootstrap; Kernel Smoothing; U−statistic;
- C14: Semiparametric and Nonparametric Methods: General
- C52: Model Evaluation, Validation, and Selection
Pascal Lavergne, Samuel Maistre, and Valentin Patilea, “A Significance Test for Covariates in Nonparametric Regression”, Electronic Journal of Statistics, vol. 9, 2015, pp. 643–678.
TSE Working Paper, n. 14-502, March 2014