Adaptive wavelet multivariate regression with errors in variables

被引：9

作者：

Chichignoud, Michael ^{[1
]}

Hoang, Van Ha ^{[2
]}

Thanh Mai Pham Ngoc ^{[3
]}

Rivoirard, Vincent ^{[4
]}

机构：

[1] Swiss Fed Inst Technol, Zurich, Switzerland

[2] Univ Sci & Technol Lille 1, Lab Paul Painleve, UMR CNRS 8524, F-59655 Villeneuve Dascq, France

[3] Univ Paris 11, UMR 8628, Lab Math, F-91405 Orsay, France

[4] PSL Res Univ, Univ Paris Dauphine, UMR 7534, CEREMADE,CNRS, F-75016 Paris, France

来源：

ELECTRONIC JOURNAL OF STATISTICS | 2017年 / 11卷 / 01期

基金：

瑞士国家科学基金会;

关键词：

Adaptive wavelet estimator; anisotropic regression; deconvolution; measurement errors; NONPARAMETRIC REGRESSION; DENSITY-ESTIMATION; DECONVOLUTION; INEQUALITIES; MODELS;

D O I：

10.1214/17-EJS1238

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In the multidimensional setting, we consider the errors-invariables 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 Holder classes. Our theoretical results are illustrated by some simulations.

引用

页码：682 / 724

页数：43

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