LAD-Liu-Lasso for robust estimation and variable selection in linear regression models

GENÇ M., Lukman A.

Journal of Applied Statistics, 2026 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1080/02664763.2026.2680091
  • Dergi Adı: Journal of Applied Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Aerospace Database, Applied Science & Technology Source, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO), Business Source Ultimate (EBSCO), Health Research Premium Collection (ProQuest), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
  • Anahtar Kelimeler: high-dimensional regression, LAD-Liu-Lasso, Least absolute deviation, Liu-Lasso estimator, robust variable selection, shrinkage estimation
  • Çukurova Üniversitesi Adresli: Evet

Özet

We employed the Least absolute shrinkage and selection operator (Lasso) for shrinkage estimation and variable selection, but it is sensitive to outliers. On the other hand, the Least absolute deviation (LAD) regression is robust but lacks uniqueness in high-dimensional modeling. Therefore, there is a clear need for robust regression methods tailored to high-dimensional data. One effective solution is to combine LAD regression with Lasso methods, creating the LAD-Lasso regression. Recent research has shown that the Liu-Lasso estimator outperforms LASSO, as it integrates the penalization functions of the Liu estimator with those of Lasso. Studies indicate that Liu-Lasso automatically selects variables and demonstrates significant predictive performance with minimal mean squared error across sparse and non-sparse data structures. Building on this, we propose a robust version of Liu-Lasso called LAD-Liu-Lasso, inspired by the LAD-Lasso approach. We compared LAD-Liu-Lasso with the Least Squares method, Liu estimator, LAD regression, and LAD-Lasso. Additionally, LAD-Liu-Lasso benefits from easily estimated tuning parameters and maintains the same asymptotic efficiency as the unpenalized LAD estimator. Extensive simulation studies confirm the satisfactory finite-sample performance of LAD-Liu-Lasso, and we provide two real examples for illustration.