Analysis of the rate of convergence of least squares neural network regression estimates in case of measurement errors

被引：12

作者：

Kohler, Michael ^{[1
]}

Mehnert, Jens ^{[1
]}

机构：

[1] Tech Univ Darmstadt, Fachbereich Math, D-64289 Darmstadt, Germany

来源：

NEURAL NETWORKS | 2011年 / 24卷 / 03期

关键词：

Least squares estimates; Measurement error; Neural networks; Rate of convergence; Regression estimates; L-2; error; NONPARAMETRIC REGRESSION; BOUNDS;

D O I：

10.1016/j.neunet.2010.11.003

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Estimation of a regression function from data which consists of an independent and identically distributed sample of the underlying distribution with additional measurement errors in the independent variables is considered. It is allowed that the measurement errors are not independent and have a nonzero mean. It is shown that the rate of convergence of suitably defined least squares neural network estimates applied to this data is similar to the rate of convergence of least squares neural network estimates applied to an independent and identically distributed sample of the underlying distribution as long as the measurement errors are small. (C) 2011 Published by Elsevier Ltd

引用

页码：273 / 279

页数：7

共 23 条

[1]

[Anonymous], 1996, Probability Theory

[2]

Anthony M., 1999, Neural Networks and Learning: Theoretical Foundations

[3] An L2-Boosting Algorithm for Estimation of a Regression Function [J].

Bagirov, Adil M. ;

Clausen, Conny ;

Kohler, Michael .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2010, 56 (03) :1417-1429

[4] STATISTICAL PROPERTIES OF ARTIFICIAL NEURAL NETWORKS [J].

BARRON, AR .

PROCEEDINGS OF THE 28TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-3, 1989, :280-285

[5] UNIVERSAL APPROXIMATION BOUNDS FOR SUPERPOSITIONS OF A SIGMOIDAL FUNCTION [J].

BARRON, AR .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1993, 39 (03) :930-945

[6]

BARRON AR, 1991, NATO ADV SCI I C-MAT, V335, P561

[7] Nonparametric regression in the presence of measurement error [J].

Carroll, RJ ;

Maca, JD ;

Ruppert, D .

BIOMETRIKA, 1999, 86 (03) :541-554

[8]

Cybenko G., 1989, Mathematics of Control, Signals, and Systems, V2, P303, DOI 10.1007/BF02551274

[9] Nonparametric regression estimation in the heteroscedastic errors-in-variables problem [J].

Delaigle, Aurore ;

Meister, Alexander .

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2007, 102 (480) :1416-1426

[10] A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem [J].

Delaigle, Aurore ;

Fan, Jianqing ;

Carroll, Raymond J. .

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2009, 104 (485) :348-359

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