Open Access
2011 Robust regression through the Huber’s criterion and adaptive lasso penalty
Sophie Lambert-Lacroix, Laurent Zwald
Electron. J. Statist. 5: 1015-1053 (2011). DOI: 10.1214/11-EJS635


The Huber’s Criterion is a useful method for robust regression. The adaptive least absolute shrinkage and selection operator (lasso) is a popular technique for simultaneous estimation and variable selection. The adaptive weights in the adaptive lasso allow to have the oracle properties. In this paper we propose to combine the Huber’s criterion and adaptive penalty as lasso. This regression technique is resistant to heavy-tailed errors or outliers in the response. Furthermore, we show that the estimator associated with this procedure enjoys the oracle properties. This approach is compared with LAD-lasso based on least absolute deviation with adaptive lasso. Extensive simulation studies demonstrate satisfactory finite-sample performance of such procedure. A real example is analyzed for illustration purposes.


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Sophie Lambert-Lacroix. Laurent Zwald. "Robust regression through the Huber’s criterion and adaptive lasso penalty." Electron. J. Statist. 5 1015 - 1053, 2011.


Published: 2011
First available in Project Euclid: 15 September 2011

zbMATH: 1274.62467
MathSciNet: MR2836768
Digital Object Identifier: 10.1214/11-EJS635

Keywords: Adaptive LASSO , concomitant scale , Huber’s criterion , oracle property , robust estimation

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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