Adaptive wavelet multivariate regression with errors in variables

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

Document type :

Article dans une revue scientifique: Article original

Title :

Adaptive wavelet multivariate regression with errors in variables

Author(s) :

Chichignoud, Michaël [Auteur]
Seminar for Statistics [ETH Zürich] [SfS]
Hoang, van Ha [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Pham Ngoc, Thanh Mai [Auteur]
Laboratoire de Mathématiques d'Orsay [LMO]
Rivoirard, Vincent [Auteur]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

Journal title :

Electronic Journal of Statistics

Pages :

682-724

Publisher :

Shaker Heights, OH : Institute of Mathematical Statistics

Publication date :

2017-03-09

ISSN :

1935-7524

HAL domain(s) :

Mathématiques [math]/Statistiques [math.ST]

English 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 ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Calibration statistique

Collections :