  In the multidimensional setting, we consider the errors-in-variables model.
We aim at estimating the unknown nonparametric multivariate regression function
with errors in the covariates. We devise an adaptive estimator based on
projection kernels on wavelets and a deconvolution operator. We propose an
automatic and fully data driven procedure to select the wavelet level
resolution. We obtain an oracle inequality and optimal rates of convergence
over anisotropic H{\"o}lder classes. Our theoretical results are illustrated by
some simulations.
