Weighted LAD-Liu-LASSO for robust estimation and sparsity

Murat Genç () and Adewale Lukman ()
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Murat Genç: Tarsus University
Adewale Lukman: University of North Dakota

Computational Statistics, 2025, vol. 40, issue 9, No 8, 5075-5104

Abstract: Abstract The Least Absolute Shrinkage and Selection Operator (LASSO) is widely used for parameter estimation and variable selection but can encounter challenges with outliers and heavy-tailed error distributions. Integrating variable selection methods such as LASSO with Weighted Least Absolute Deviation (WLAD) has been explored in limited studies to handle these problems. In this study, we proposed the integration of Weighted Least Absolute Deviation with Liu-LASSO to handle variable selection, parameter estimation, and heavy-tailed error distributions due to the advantages of the Liu-LASSO approach over traditional LASSO methods. This approach is demonstrated through a simple simulation study and real-world application. Our findings showcase the superiority of our method over existing techniques while maintaining the asymptotic efficiency comparable to the unpenalized LAD estimator.

Keywords: Lasso; Least absolute deviation; Weighted estimator; Liu-Lasso; Outliers; Variable selection (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00180-025-01605-6

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