Adaptive wavelet multivariate regression with errors in variables

Chichignoud, Michaël; Hoang, Van Ha; Pham Ngoc, Thanh Mai; Rivoirard, Vincent

Chichignoud, Michaël; Hoang, Van Ha; Pham Ngoc, Thanh Mai; Rivoirard, Vincent (2017), Adaptive wavelet multivariate regression with errors in variables, Electronic Journal of Statistics, 11, 1, p. 682-724. 10.1214/17-EJS1238

Type

Article accepté pour publication ou publié

External document link

https://hal.archives-ouvertes.fr/hal-01253508

Date

2017

Journal name

Electronic Journal of Statistics

Volume

Number

Publisher

Institute of Mathematical Statistics

Published in

Paris

Pages

682-724

Abstract (EN)

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 Hölder classes. Our theoretical results are illustrated by some simulations.

Subjects / Keywords

Adaptive wavelet estimator; Anisotropic regression; Deconvolution; Measurement errors

JEL

C14 - Semiparametric and Nonparametric Methods: General