ABSTRACT
This chapter explains the number of techniques for smoothing a response variable on one or more predictor variables. It describes more deeply into the smoothing problem, investigating a number of topics of both practical and theoretical importance. In scatterplot smoothing there is a fundamental trade-off between the bias and variance of the estimate, and this trade-off is governed by the smoothing parameter. The analysis of a linear scatterplot smoother through an eigen-analysis of the corresponding smoother matrix is closely related to the study of the transfer function of a linear filter for time series. Silverman and discussants covered a broad range of topics including a theoretical comparison of smoothing splines and kernel smoothers, a finite sample Bayesian model, and efficient computation of the cross-validation scores. The running-mean, running-line, smoothing spline, kernel, locally-weighted running-line and regression spline smoothers are all linear smoothers.
