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We consider testing the significance of a subset of covariates in anonparametric regression. These covariates can be continuous and/or discrete.We propose a new kernel-based test that smoothes only over the covariatesappearing under the null hypothesis, so that the curse of dimensionality ismitigated. The test statistic is asymptotically pivotal and the rate of whichthe test detects local alternatives depends only on the dimension of thecovariates under the null hypothesis. We show the validity of wild bootstrapfor the test. In small samples, our test is competitive compared to existingprocedures.

A Significance Test for Covariates in Nonparametric Regression