On the Use of Nonparametric Regression in Assessing Parametric Regression Models

Abstract

We develop a new method for assessing the adequacy of a smooth regression function based on nonparametric regression and the bootstrap. Our methodology allows users to detect systematic misfit and to test hypotheses of the form “the proposed smooth regression model is not significantly different from the smooth regression model that generated these data.” We also provide confidence bands on the location of nonparametric regression estimates assuming that the proposed regression function is true, allowing users to pinpoint regions of misfit. We illustrate the application of the new method, using local linear nonparametric regression, both where an error model is assumed and where the error model is an unknown non-stationary function of the predictor.