Robust LASSO and Its Applications in Healthcare Data

Abstract

We address the development of a robust variable selection procedure using the density power divergence with the least absolute shrinkage and selection operator (LASSO). It produces robust estimates of the regression parameters and simultaneously selects the important explanatory variables. The asymptotic distribution of the regression coefficients is derived. The widely used model selection procedures based on the classical information criteria often show very poor performance in the presence of heavy-tailed error or outliers. For this purpose, we introduce a robust version of the Mallows’s $C_p$ statistic based on our proposed method. The simulation studies show that the robust variable selection technique outperforms the classical likelihood-based techniques in the presence of outliers. The performance of the proposed method is explored through a healthcare data analysis.