Introduction

Until now we have confined discussion to scatterplot smoothers. This setting served well to illustrate the main concepts behind smoothing. However, there is a gap between the methodology and the needs of practitioners. As exemplified by the problems described in Chapter 1, most applications of regression involve several predictors. To begin closing the gap, this chapter introduces a class of multiple regression models that have a nonparametric component involving only a single predictor and a parametric component for the other predictors. Having both parametric and nonparametric components means the models are semiparametric. This class of simple semiparametric models is important in its own right but also serves as an introduction to more complex semiparametric regression models of later chapters, where the effects of several predictors are modeled nonparametrically.

Beyond Scatterplot Smoothing

The end of the previous chapter closed off quite a lengthy description of how to smooth out a scatterplot and perform corresponding inference. In Chapter 3 we described three general approaches: penalized splines, local polynomial fitting, and series approximation. For penalized splines, we presented both an algorithmic approach based on ridge regression and a mixed model approach based on maximum likelihood and best prediction. There are other approaches to scatterplot smoothing that we did not describe at all.