Adaptive wavelet multivariate regression with errors in variables
Statistics Theory
2016-01-13 v1 Statistics Theory
Abstract
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.
Cite
@article{arxiv.1601.02762,
title = {Adaptive wavelet multivariate regression with errors in variables},
author = {Michaël Chichignoud and Van Ha Hoang and Thanh Mai Pham Ngoc and Vincent Rivoirard},
journal= {arXiv preprint arXiv:1601.02762},
year = {2016}
}