Testing Lack-of-fit of Parametric Regression Models Using Nonparametric Regression Techniques

Data-driven lack-of-fit tests are derived for parametric regression models using fit comparison statistics that are based on nonparametric linear smoothers. The tests are applicable to settings where the usual bandwidth/smoothing parameter asymptotics apply to the null model, which includes testing for nonlinear models and some linear models. Large sample distribution theory is established for tests constructed from both kernel and series type estimators. Both types of smoothers are shown to give consistent tests that are asymptotically normal under the null model after appropriate centering and scaling. However, the projection nature of series smoothers results in a simplified scaling factor that produces computational savings for the associated tests.