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December, 1990 Adaptive $M$-Estimation in Nonparametric Regression
Peter Hall, M. C. Jones
Ann. Statist. 18(4): 1712-1728 (December, 1990). DOI: 10.1214/aos/1176347874

Abstract

A method for robust nonparametric regression is discussed. We consider kernel $M$-estimates of the regression function using Huber's $\psi$-function and extend results of Hardle and Gasser to the case of random designs. A practical adaptive procedure is proposed consisting of simultaneously minimising a cross-validatory criterion with respect to both the smoothing parameter and a robustness parameter occurring in the $\psi$-function. This method is shown to possess a theoretical asymptotic optimality property, while some simulated examples confirm that the approach is practicable.

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Peter Hall. M. C. Jones. "Adaptive $M$-Estimation in Nonparametric Regression." Ann. Statist. 18 (4) 1712 - 1728, December, 1990. https://doi.org/10.1214/aos/1176347874

Information

Published: December, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0737.62034
MathSciNet: MR1074431
Digital Object Identifier: 10.1214/aos/1176347874

Subjects:
Primary: 62G05
Secondary: 62F35

Keywords: cross-validation , Huber's $\psi$-function , Kernel estimation , robust smoothing

Rights: Copyright © 1990 Institute of Mathematical Statistics

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Vol.18 • No. 4 • December, 1990
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