## Electronic Journal of Statistics

### Adaptive wavelet multivariate regression with errors in variables

#### 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 estimators 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.

#### Article information

Source
Electron. J. Statist., Volume 11, Number 1 (2017), 682-724.

Dates
First available in Project Euclid: 8 March 2017

https://projecteuclid.org/euclid.ejs/1488964114

Digital Object Identifier
doi:10.1214/17-EJS1238

Mathematical Reviews number (MathSciNet)
MR3620733

Zentralblatt MATH identifier
1362.62086

Subjects
Primary: 62G08: Nonparametric regression

#### Citation

Chichignoud, Michaël; Hoang, Van Ha; Pham Ngoc, Thanh Mai; Rivoirard, Vincent. Adaptive wavelet multivariate regression with errors in variables. Electron. J. Statist. 11 (2017), no. 1, 682--724. doi:10.1214/17-EJS1238. https://projecteuclid.org/euclid.ejs/1488964114

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