The problem of deciding how much to smooth is of great importance in nonparametric regression. Before embarking on technical solutions of the problem it is worth noting that a selection of the smoothing parameter is always related to a certain interpretation of the smooth. If the purpose of smoothing is to increase the “signal to noise ratio” for presentation, or to suggest a simple (parametric) models, then a slightly “oversmoothed” curve with a subjectively chosen smoothing parameter might be desirable. On the other hand, when the interest is purely in estimating the regression curve itself with an emphasis on local structures then a slightly “undersmoothed” curve may be appropriate.

However, a good automatically selected parameter is always a useful starting (view)point. An advantage of automatic selection of the band-width for kernel smoothers is that comparison between laboratories can be made on the basis of a standardized method. A further advantage of an automatic method lies in the application of additive models for investigation of high-dimensional regression data. For complex iterative procedures such as projection pursuit regression (Friedman and Stuetzle 1981) or ACE (Breiman and Friedman 1985) it is vital to have a good choice of smoothing parameter for one-dimensional smoothers that are elementary building blocks for these procedures.