Checking the adequacy of a partial linear model

A partial linear model is a model where the response variable depends on some covariates linearly and on others nonparametrically. In this article, we construct an empirical process-based test for examining the adequacy of partial linearity of model. A re-sampling approach, called random symmetrization (RS), 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.