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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.

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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
Mathematics, Computing and Technology
Item ID: 28321
Depositing User: Sarah Frain
Date Deposited: 22 Mar 2011 11:33
Last Modified: 18 Jan 2016 10:06
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