Robust adaptive Lasso for variable selection

Qi Zheng, Colin Gallagher and K. B. Kulasekera

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 9, 4642-4659

Abstract: The adaptive least absolute shrinkage and selection operator (Lasso) and least absolute deviation (LAD)-Lasso are two attractive shrinkage methods for simultaneous variable selection and regression parameter estimation. While the adaptive Lasso is efficient for small magnitude errors, LAD-Lasso is robust against heavy-tailed errors and severe outliers. In this article, we consider a data-driven convex combination of these two modern procedures to produce a robust adaptive Lasso, which not only enjoys the oracle properties, but synthesizes the advantages of the adaptive Lasso and LAD-Lasso. It fully adapts to different error structures including the infinite variance case and automatically chooses the optimal weight to achieve both robustness and high efficiency. Extensive simulation studies demonstrate a good finite sample performance of the robust adaptive Lasso. Two data sets are analyzed to illustrate the practical use of the procedure.

Date: 2017
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DOI: 10.1080/03610926.2015.1019138

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