文章基本信息

标题：Robust regression through the Huber’s criterion and adaptive lasso penalty
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作者：Sophie Lambert-Lacroix ; Laurent Zwald
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2011
卷号：5
页码：1015-1053
DOI：10.1214/11-EJS635
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.
关键词：Adaptive lasso;concomitant scale;Huber’s cri terion;oracle property;robust estimation.