A Simple Goodness-of-Fit Test for Parametric Regression Models

Abstract

A simple test is proposed for examining the adequacy of a family of parametric models against nonparametric alternatives. The usual diagnostic tools based on the residuals plots are useful but do not lead to formal statistical tests. We propose a formal statistical test that complements the graphical analysis. Technically, the possible bias of the residuals of the parametric fit is assumed to be a squared summable function of the predictive variable and is decomposed along a family of orthogonal polynomials. Our simulation studies indicate that this test has a similar power as that of the adaptative Neyman test. Moreover, it is simple to put on using usual statistical software and may be easily extended to generalized linear and partial linear models.