ABSTRACT
This chapter provides a brief summary which is given of the key methods available for univariate nonparametric regression function estimation. Different techniques are like different hardware tools, having different strengths in their domains of applications. A large literature has been devoted to scatter plot smoothing, where the domain of the data is the same as that of human visualization. Two data sets will be used to illustrate some of the methods. The first consists of 133 observations of motorcycle data presented. The second data set concerns 435 adults suffering from burn injuries. In comparison with the local linear fit, the Nadaraya-Watson estimator locally uses one parameter less without reducing the asymptotic variance. This extra parameter enables the local linear fit to reduce the bias. A technique closely related to nonparametric regression is density estimation. It is used to examine the overall pattern of a data set.
