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.


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