A Consistent Model Specification Test for Nonparametric Estimation of Regression Function Models

This paper proposes a general framework for specification testing of the regression function in a nonparametric smoothing estimation context. The same analysis can be applied to cases as varied as testing for omission of variables, testing certain nonlinear restrictions in the regressors, and testing the correct specification of some parametric or semiparametric model of interest, for example, testing a certain type of nonlinearity of the regression function. Furthermore, the test can be applied to i.i.d. and time-series data, and some or all of the regressors are allowed to be discrete. A Monte Carlo simulation is used to assess the performance of the test in small and medium samples.