Nonparametric significance testing

A procedure for testing the signicance of a subset of explanatory variables in a nonparametric regression is proposed. Our test statistic uses the kernel method. Under the null hypothesis of no effect of the variables under test, we show that our test statistic has a nhp2/2 standard normal limiting distribution, where p2 is the dimension of the complete set of regressors. Our test is one-sided, consistent against all alternatives and detect local alternatives approaching the null at rate slower than n-1/2 h-p2/4. Our Monte-Carlo experiments indicate that it outperforms the test proposed by Fan and Li (1996).