Electronic Journal of Statistics

Adaptive wavelet multivariate regression with errors in variables

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

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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
Received: January 2016
First available in Project Euclid: 8 March 2017

Permanent link to this document
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

Keywords
Adaptive wavelet estimator anisotropic regression deconvolution measurement errors

Rights
Creative Commons Attribution 4.0 International License.

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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