On the use of nonparametric regression for model checking

Abstract

The use of nonparametric regression is explored to check the fit of a parametric regression model. The principal aim is to check the validity of the regression curve rather than necessarily to detect outliers. A pseudo likelihood ratio test is developed to provide a global assessment of fit and simulation bands are used to indicate the nature of departures from the model. The types of data considered include discrete response variables, where standard diagnostic techniques are often not appropriate, and first-order autoregressive series. Several numerical examples are given.