Adaptive wavelet multivariate regression with errors in variables

2016/01/12 by Michaël Chichignoud, Chichignoud, Michaël, Van Ha Hoang +5 · 2 citations
Mathematics · #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1601.02762

arxiv created 2016/01/12 · arxiv updated 2016/01/13

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 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.

Cited by

• Adaptive estimation for nonparametric circular regression with errors in variables
• Adaptive estimation in regression models for weakly dependent data and explanatory variable with known density

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