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Nonparametric Regression Methods

  • Hans-Georg Müller
Part of the Lecture Notes in Statistics book series (LNS, volume 46)

Abstract

Besides kernel estimators, commonly used nonparametric regression estimators are local least squares estimators and smoothing splines. Besides these estimators, we also discuss orthogonal series estimators which have been applied mainly in density estimation. All these estimators are localized weighted averages of the data, i.e. linear in the observations (Yi). The general form is
$$ \hat g{\text{L}}\left( {\text{t}} \right) = \sum\limits_{i = 1}^n {W_i } ,{\text{n}}\left( {\text{t}} \right){\text{Y}}_i ,{\text{n}} $$
with weight functions Wi,n(t), and different estimates differ only with respect to the weight functions. As we will see, the estimators considered do not differ too much and asymptotically they are all equivalent to more or less complicated kernel estimators. Therefore, kernel estimators are very general and also the method which is most easily understood intuitively.

Keywords

Smoothing Parameter Nonparametric Regression Kernel Estimate Kernel Estimator Smoothing Spline 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Hans-Georg Müller
    • 1
    • 2
  1. 1.Institute of Medical StatisticsUniversity of Erlangen-NürnbergErlangenFederal Republic of Germany
  2. 2.Division of StatisticsUniversity of CaliforniaDavisUSA

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