Adaptive wavelet multivariate regression with errors in variables

Michaël Chichignoud (1) , van Ha Hoang (2) , Thanh Mai Pham Ngoc (3) , Vincent Rivoirard (4)

1 SfS - Seminar for Statistics [ETH Zürich]
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay
4 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Domaines: Statistiques [math.ST]

Michaël Chichignoud, van Ha Hoang, Thanh Mai Pham Ngoc, Vincent Rivoirard. Adaptive wavelet multivariate regression with errors in variables. Electronic Journal of Statistics , 2017, 11 (1), pp.682-724. ⟨hal-01253508v2⟩