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An Introduction to Dimension Reduction in Nonparametric KernelRegression

Published online by Cambridge University Press:  23 January 2015

S. Girard  and
J. Saracco
S. Girard
Affiliation:
Inria Grenoble Rhône-Alpes & Laboratoire Jean Kuntzmann, France
J. Saracco
Affiliation:
Institut Polytechnique de Bordeaux & Inria Bordeaux Sud Ouest & Institut de Mathématiques de Bordeaux, France
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Abstract

Nonparametric regression is a powerful tool to estimate nonlinear relations between some predictors and a response variable. However, when the number of predictors is high, nonparametric estimators may suffer from the curse of dimensionality. In this chapter, we show how a dimension reduction method (namely Sliced Inverse Regression) can be combined with nonparametric kernel regression to overcome this drawback. The methods are illustrated both on simulated datasets as well as on an astronomy dataset using the R software.

Type
Research Article
Information
European Astronomical Society Publications Series , Volume 66: Statistics for Astrophysics Methods and Applications of the Regression , 2014 , pp. 167 - 196
Copyright
© EAS, EDP Sciences, 2015

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