Nonparametric estimation of regression level sets
Résumé
Let $(X,Y)$ be a random pair taking values in ${\R^d}\times J$, where $J\subset\R$ is supposed to be bounded. We propose a plug-in estimator of the level sets of a regression function $r$ of $Y$ on $X$, using a kernel estimator of $r$. We consider an error criterion defined by the volume of the symmetrical difference between the real and estimated level sets. We state the consistency of our estimator, and we get a rate of convergence equivalent to the one obtained by Cadre for the density function level sets. Finally we discuss the practical results obtained with a simulated data set.
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