Weighted LAD-LASSO method for robust parameter estimation and variable selection in regression

Abstract

The weighted least absolute deviation (WLAD) regression estimation method and the adaptive least absolute shrinkage and selection operator (LASSO) are combined to achieve robust parameter estimation and variable selection in regression simultaneously. Compared with the LAD-LASSO method, the weighted LAD-LASSO (WLAD-LASSO) method will resist to the heavy-tailed errors and outliers in explanatory variables. Properties of the WLAD-LASSO estimators are investigated. A small simulation study and an example are provided to demonstrate the superiority of the WLAD-LASSO method over the LAD-LASSO method in the presence of outliers in the explanatory variables and the heavy-tailed error distribution.