ABSTRACT
Smoothing or non-parametric function estimation was one of the largest areas of statistical research in the 1980s, and is now a recognized tool for exploratory data analysis. In regression problems, instead of fitting a simple linear model
E(y|x) = β0 + β1x, we fit a non-parametric smooth or simply a smooth approach to data:
E(y|x) = f(x) where f(x) is an arbitrary smooth function. Smoothness of the function is a key requirement, as otherwise the estimate may have excessive variation that masks interesting underlying patterns. The model is nonparametric in that is has no easily interpretable parameters as in a linear model, but as we shall see, the estimation of f(x) implicitly involves some estimation of parameters. One crucial issue in all smoothing problems is how much to smooth; it is a problem that has given rise to a lot of theoretical developments.
