Automatic Smoothing Parameter Selection: A Survey

This is a survey of recent developments in smoothing parameter selection for curve estimation. The first goal of this paper is to provide an introduction to the methods available, with discussion at both a practical and also a nontechnical level, including comparison of methods. The second goal is to provide access to the literature, especially on smoothing parameter selection, but also on curve estimation in general. The two main settings considered here are nonparametric regression and probability density estimation, although the points made apply to other settings as well. These points also apply to many different estimators, although the focus is on kernel estimators, because they are the most easily understood and motivated, and have been at the heart of the development in the field.