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An introduction to dimension reduction in nonparametric kernel regression

Stéphane Girard 1 Jerôme Saracco 2, 3, 4
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
2 CQFD - Quality control and dynamic reliability
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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.
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Stéphane Girard, Jerôme Saracco. An introduction to dimension reduction in nonparametric kernel regression. D. Fraix-Burnet; D. Valls-Gabaud. Regression methods for astrophysics, 66, EDP Sciences, pp.167-196, 2014, EAS Publications Series, ⟨10.1051/eas/1466012⟩. ⟨hal-00977512⟩

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