The adaptive BerHu penalty in robust regression

• Published in: Journal of nonparametric statistics Vol. 28; no. 3; pp. 487 - 514
• Main Authors: Lambert-Lacroix, Sophie, Zwald, Laurent
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.07.2016; Taylor & Francis Ltd; American Statistical Association
• Subjects: adaptive BerHu penalty; Applications; concomitant scale; Estimators; Huber's criterion; Mathematical models; Nonparametric statistics; Norms; Operators; oracle property; Regression; Regression analysis; Ridges; robust estimation; Simulation; Statistics; Statistics Theory; elastic net penalty; Huber's criterion; concomitant scale; Adaptive BerHu penalty; oracle property; robust estimation Availability

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 pres...