Outlier detection and robust variable selection via the penalized weighted LAD-LASSO method.

Area of Science:

• Statistics
• Data Science
• Machine Learning

Background:

• Linear regression models are widely used but sensitive to outliers and leverage points.
• Robust variable selection is crucial for reliable model interpretation and prediction.
• Existing methods often struggle with simultaneous outlier detection and variable selection in contaminated datasets.

Purpose of the Study:

• To develop a robust methodology for simultaneous outlier detection and variable selection in linear regression.
• To propose an efficient iterative algorithm for solving the associated optimization problem.
• To evaluate the finite-sample performance of the proposed methods using Monte Carlo simulations.

Main Methods:

• Combining penalized weighted least absolute deviation (PWLAD) regression with adaptive least absolute shrinkage and selection operator (LASSO).
• Developing an iterative algorithm to solve the penalized optimization problem.
• Conducting Monte Carlo simulations to assess finite-sample performance.

Main Results:

• The proposed PWLAD-adaptive LASSO method effectively achieves simultaneous outlier detection and robust variable selection.
• The method shows superior finite-sample performance compared to existing techniques, particularly in the presence of leverage points or outliers.
• The methodology was successfully applied to analyze two real-world datasets, demonstrating practical utility.

Conclusions:

• The integrated PWLAD and adaptive LASSO approach offers a robust and effective solution for outlier detection and variable selection in linear regression.
• The proposed iterative algorithm provides an efficient way to implement the methodology.
• This method is particularly valuable for analyzing datasets prone to contamination.