Nonparametric estimation via empirical risk minimization

Author

Lugosi, Gábor ; Zeger, Kenneth

Author_Institution

Dept. of Math. & Comput. Sci., Tech. Univ. Budapest, Hungary

Volume

41

Issue

3

fYear

1995

fDate

5/1/1995 12:00:00 AM

Firstpage

677

Lastpage

687

Abstract

A general notion of universal consistency of nonparametric estimators is introduced that applies to regression estimation, conditional median estimation, curve fitting, pattern recognition, and learning concepts. General methods for proving consistency of estimators based on minimizing the empirical error are shown. In particular, distribution-free almost sure consistency of neural network estimates and generalized linear estimators is established

Keywords

curve fitting; estimation theory; learning (artificial intelligence); minimisation; neural nets; nonparametric statistics; pattern recognition; conditional median estimation; curve fitting; distribution-free almost sure consistency; empirical error minimisation; empirical risk minimization; generalized linear estimators; learning concepts; neural network estimates; nonparametric estimation; nonparametric estimators; pattern recognition; regression estimation; universal consistency; Computer errors; Computer science; Convergence; Curve fitting; Mathematics; Neural networks; Pattern recognition; Random variables; Risk management; Training data;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.382014

Filename

382014