Nonparametric estimation of regression level sets using kernel plug-in estimator

Let (X,Y) be a random pair taking values in Rd×J, where J⊂R is supposed to be bounded. We propose a plug-in estimator of the level sets of the 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 (2006) for the density function level sets.