An Efficient Method for Variable Selection Based on Diagnostic-Lasso Regression

In contemporary statistical methods, robust regression shrinkage and variable selection have gained paramount significance due to the prevalence of datasets characterized by contamination and an abundance of variables, often categorized as 'high-dimensional data'. The Least Absolute Shrinkage and Selection Operator (Lasso) is frequently employed in this context for both the model and selecting variables. However, no one has attempted to apply regression diagnostic measures to Lasso regression, despite its power and widespread practical use. This work introduces a combined Lasso and diagnostic technique to enhance Lasso regression modeling for high-dimensional datasets with multicollinearity and outliers. We utilize a diagnostic Lasso estimator (D-Lasso). The breakdown point of the proposed method is also discussed. Finally, simulation examples and analyses of real data are provided to support the conclusions. The results of the numerical examples demonstrate that the D-Lasso approach performs as well as, if not better than, the robust Lasso method based on the MM-estimator.