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Robust regression through the Huber’s criterion and adaptive lasso penalty. (English) Zbl 1274.62467
Summary: 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.

##### MSC:
 62J07 Ridge regression; shrinkage estimators (Lasso) 62J05 Linear regression; mixed models 62F35 Robustness and adaptive procedures (parametric inference) 62P05 Applications of statistics to actuarial sciences and financial mathematics
CVX; SeDuMi
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