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Section: New Results

An introduction to dimension reduction in nonparametric kernel regression

Participant : Jérôme Saracco.

This work is in collaboration with Stéphane Girard (Inria Grenoble Alpes).

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.

This work was presented in ”School in Astrostatistics” (Annecy, October, 21-25, 2013) and is to appear as a chapter in book intilted Methods and Applications of Regression in Astrophysics in 2014.