The Open UniversitySkip to content
 

Adaptive M-estimation in nonparametric regression

Hall, P. and Jones, Chris (1990). Adaptive M-estimation in nonparametric regression. Annals of Statistics, 18(4) pp. 1712–1728.

Google Scholar: Look up in Google Scholar

Abstract

A method for robust nonparametric regression is discussed. A method for robust nonparametric regression is discussed. We consider kernel M-estimates of the regression function using Huber's ψ-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 ψ-function. This method is shown to possess a theoretical asymptotic optimality property, while some simulated examples confirm that the approach is practicable.

Item Type: Journal Article
Copyright Holders: 1990 Institute of Mathematical Statistics
ISSN: 0090-5364
Keywords: cross-validation; Huber's ψ function; kernel estimation; robust smoothing
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 28321
Depositing User: Sarah Frain
Date Deposited: 22 Mar 2011 11:33
Last Modified: 22 Mar 2011 11:33
URI: http://oro.open.ac.uk/id/eprint/28321
Share this page:

Actions (login may be required)

View Item
Report issue / request change

Policies | Disclaimer

© The Open University   + 44 (0)870 333 4340   general-enquiries@open.ac.uk