Nonparametric significance testing

A procedure for testing the significance of a subset of explanatory variabl es in a nonparametric regression is proposed. Our test statistic uses the k ernel method. Under the null hypothesis of no effect of the variables under test, we show that our test statistic has an nh(P2/2) standard normal Limi ting distribution, where p(2) is the dimension of the complete set of regre ssors. Our test is one-sided, consistent against all alternatives and detec ts 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 prop osed by Fan and Li (1996, Econometrica 64, 865-890).