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Linear smoothers and additive models
 The Annals of Statistics
, 1989
"... We study linear smoothers and their use in building nonparametric regression models. In part Qfthis paper we examine certain aspects of linear smoothers for scatterplots; examples of these are the running mean and running line, kernel, and cubic spline smoothers. The eigenvalue and singular value d ..."
Abstract

Cited by 70 (2 self)
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We study linear smoothers and their use in building nonparametric regression models. In part Qfthis paper we examine certain aspects of linear smoothers for scatterplots; examples of these are the running mean and running line, kernel, and cubic spline smoothers. The eigenvalue and singular value decompositions of the corresponding smoother matrix are used to qualitatively describe a smoother, and several other topics such as the number of degrees of freedom of a smoother are discussed. In the second part of the paper we describe how Iinearsmoothers can be used to estimate the additive model, a powerful nonparametric regression model, using the "backfitting algorithm". We study the convergence of the backfitting algorithm and prove its convergence for a class of smoothers that includes cubic e:ttJlClâ‚¬~nt jJI:::Jll<l.li:6I;:U least squares. algorithm and ' dis.cuss ev'W()r(is: Neaparametric, seanparametric, regression, GaussSeidelalgorithm,