Data-Driven Choice of Smoothing Parameters

Abstract

This chapter is devoted to the problem of choosing the smoothing parameter of a nonparametric regression estimator, a problem that plays a major role in the remainder of this book. We will use S to denote a generic smoothing parameter when we are not referring to a particular type of smoother. The sophistication of the technique used to choose S will depend on the data analyst’s reasons for fitting a nonparametric smooth to the data. If one wishes a smooth to be merely a descriptive device, then the “by eye” technique may be satisfactory. Here, one looks at several smooths corresponding to different values of S and chooses one (or more) which display interesting features of the data. In doing so, the data analyst is not necessarily saying that these features are verification of similar ones in a population curve; he only wishes to describe aspects of the data that may warrant further investigation.