Publication Type
Journal Article
Version
publishedVersion
Publication Date
10-2005
Abstract
A popular data-driven method for choosing the bandwidth in standard kernel regression is cross-validation. Even when there are outliers ill the data, robust kernel regression can be used to estimate the unknown regression curve [Robust and Nonlinear Time Series Analysis. Lecture Notes in Statist. (1984) 26 163-184]. However, Under these Circumstances Standard cross-validation is no longer a satisfactory bandwidth selector because it is unduly influenced by extreme prediction errors caused by the existence of these Outliers. A more robust method proposed here is a cross-validation method that discounts the extreme prediction errors. In large samples the robust method chooses consistent bandwidths, and the consistency of the method is practically independent of the form ill which extreme prediction errors are discounted. Additionally, evaluation of the method's finite sample behavior in a simulation demonstrates that the proposed method performs favorably. This method call also be applied to other problems, for example, model selection, that require cross-validation.
Keywords
Bandwidth, cross-validation, kernel, nonparametric regression, robust, smoothing
Discipline
Econometrics
Research Areas
Econometrics
Publication
Annals of Statistics
Volume
33
Issue
5
First Page
2291
Last Page
2310
ISSN
0090-5364
Identifier
10.1214/009053605000000499
Publisher
Institute of Mathematical Statistics
Citation
Leung, Denis H. Y..
Cross-Validation in Nonparametric Regression with Outliers. (2005). Annals of Statistics. 33, (5), 2291-2310.
Available at: https://ink.library.smu.edu.sg/soe_research/127
Copyright Owner and License
Publisher
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1214/009053605000000499