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Nonparametric significance testing. (English) Zbl 0968.62047
Summary: A procedure for testing the significance 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 an \(nh^{p_2/2}\) standard normal limiting distribution, where \(p_2\) is the dimension of the complete set of regressors. Our test is one-sided, consistent against all alternatives and detects local alternatives approaching the null at rate slower than \(n^{-1/2} h^{-p_2/4}\). Our Monte-Carlo experiments indicate that it outperforms the test proposed by Y. Fan and Q. Li [Econometrica 64, No. 4, 865-890 (1996; Zbl 0854.62038)].

MSC:
62G10 Nonparametric hypothesis testing
62G08 Nonparametric regression and quantile regression
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