Variable selection and parameter estimation via WLAD-SCAD with a diverging number of parameters

In this paper, we focus on the variable selection based on the weighted least absolute deviation (WLAD) regression with the diverging number of parameters. The WLAD estimator and the smoothly clipped absolute deviation (SCAD) are combined to achieve robust parameter estimation and variable selection in regression simultaneously. Compared with the LAD-SCAD method, the WLAD-SCAD method will resist the heavy-tailed errors and outliers in explanatory variables. Furthermore, we obtain consistency and asymptotic normality of the estimators under certain appropriate conditions. Simulation studies and a real example are provided to demonstrate the superiority of the WLAD-SCAD method over the other regularization methods in the presence of outliers in the explanatory variables and the heavy-tailed error distribution.