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Robust Regression through the Huber's criterion and adaptive lasso penalty
Abstract : 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 er- rors 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.
Cited literature [37 references]
https://hal.archives-ouvertes.fr/hal-00661864
Contributor : Laurent Zwald Connect in order to contact the contributor
Submitted on : Friday, January 20, 2012 - 6:14:44 PM
Last modification on : Wednesday, February 2, 2022 - 12:30:01 PM
Long-term archiving on: : Saturday, April 21, 2012 - 2:41:41 AM
Contributor : Laurent Zwald Connect in order to contact the contributor
Submitted on : Friday, January 20, 2012 - 6:14:44 PM
Last modification on : Wednesday, February 2, 2022 - 12:30:01 PM
Long-term archiving on: : Saturday, April 21, 2012 - 2:41:41 AM
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