Checking the adequacy of a partial linear model. (English) Zbl 1028.62032

Summary: A partial linear model is a model where the response variable depends on some covariates linearly and on others nonparametrically. We construct an empirical process-based test for examining the adequacy of partial linearity of models. A re-sampling approach, called random symmetrization, is applied to obtain the approximation to the null distribution of the test. The procedure is easy to implement. A simulation study is carried out and application to an example is made.


62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
62G08 Nonparametric regression and quantile regression