The adaptive BerHu penalty in robust regression

Sophie Lambert-Lacroix and Laurent Zwald

Journal of Nonparametric Statistics, 2016, vol. 28, issue 3, 487-514

Abstract: We intend to combine Huber's loss with an adaptive reversed version as a penalty function. The purpose is twofold: first we would like to propose an estimator that is robust to data subject to heavy-tailed errors or outliers. Second we hope to overcome the variable selection problem in the presence of highly correlated predictors. For instance, in this framework, the adaptive least absolute shrinkage and selection operator (lasso) is not a very satisfactory variable selection method, although it is a popular technique for simultaneous estimation and variable selection. We call this new penalty the adaptive BerHu penalty. As for elastic net penalty, small coefficients contribute through their norm to this penalty while larger coefficients cause it to grow quadratically (as ridge regression). We will show that the estimator associated with Huber's loss combined with the adaptive BerHu penalty enjoys theoretical properties in the fixed design context. This approach is compared to existing regularisation methods such as adaptive elastic net and is illustrated via simulation studies and real data.

Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/10485252.2016.1190359 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:gnstxx:v:28:y:2016:i:3:p:487-514

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/GNST20

DOI: 10.1080/10485252.2016.1190359

Access Statistics for this article

Journal of Nonparametric Statistics is currently edited by Jun Shao

More articles in Journal of Nonparametric Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().