Hall, P. and Jones, Chris
(1990).
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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: | Article |
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| Copyright Holders: | 1990 Institute of Mathematical Statistics |
| ISSN: | 0090-5364 |
| Keywords: | cross-validation; Huber's ψ function; kernel estimation; robust smoothing |
| Academic Unit/School: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |
| Item ID: | 28321 |
| Depositing User: | Sarah Frain |
| Date Deposited: | 22 Mar 2011 11:33 |
| Last Modified: | 04 Oct 2016 11:01 |
| URI: | http://oro.open.ac.uk/id/eprint/28321 |
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