## 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