Robust Regression Estimation and Variable Selection when Cellwise and Casewise Outliers Are Present

Two main issues regarding a regression analysis are estimation and variable selection in presence of outliers. Popular robust regression estimation methods are combined with variable selection methods to simultaneously achieve robust estimation and variable selection. However, recent works showed that the robust estimation methods used in those estimation and variable selection procedures are only resistant to the casewise (rowwise) outliers in the data. Therefore, since these robust variable selection methods may not be able to cope with cellwise outliers in the data, some extra care should be taken when cellwise outliers are present along with the casewise outliers. In this study, we proposed a robust estimation and variable selection method to deal with both cellwise and casewise outliers in the data. The proposed method has three steps. In the first step, cellwise outliers were identified, deleted and marked with NA sign in each explanatory variable. In the second step, the cells with NA signs were imputed using a robust imputation method. In the last step, robust regression estimation methods were combined with the variable selection method LASSO (Least Angle Solution and Selection Operator) to estimate the regression parameters and to select remarkable explanatory variables. The simulation results and real data example revealed that the proposed estimation and variable selection procedure perform well in the presence of cellwise and casewise outliers.