×

Testing linearity for nonparametric component of partially linear models. (English) Zbl 1125.62044

Summary: In the problem of testing whether the nonparametric component of a partially linear model is a polynomial of a certain degree (denoted \(p\)), we propose a simple test statistic which is based on the sample variance of the estimated \(p\) th derivative of the nonparametric function at each design point. Three-moment \(\chi^2\) approximation is employed to derive the \(p\)-value of the test. Furthermore, some simulations are conducted to examine the performance of our test procedure and the results are satisfactory.

MSC:

62G10 Nonparametric hypothesis testing
62G08 Nonparametric regression and quantile regression
PDF BibTeX XML Cite