EAS Publications Series
Volume 66, 2014Statistics for Astrophysics Methods and Applications of the Regression
|Page(s)||167 - 196|
|Published online||23 January 2015|
D. Fraix-Burnet and D. Valls-Gabaud (eds)
EAS Publications Series, 66 (2014) 167–196
An Introduction to Dimension Reduction in Nonparametric Kernel Regression
1 Inria Grenoble Rhône-Alpes & Laboratoire Jean Kuntzmann, France
2 Institut Polytechnique de Bordeaux & Inria Bordeaux Sud Ouest & Institut de Mathématiques de Bordeaux, France
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.
© EAS, EDP Sciences, 2015
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