A significance test for covariates in nonparametric regression

Pascal Lavergne, Samuel Maistre, Valentin Patilea
2015 Electronic Journal of Statistics  
We consider testing the significance of a subset of covariates in a nonparametric 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 hypothesis. We show the
more » ... sis. We show the validity of wild bootstrap for the test. In small samples, our test is competitive compared to existing procedures. MSC 2010 subject classifications: Primary 62G08, 62G10; secondary 62G20.
doi:10.1214/15-ejs1005 fatcat:k74diaewmfae5k2aei4q3z6eiq