A Novel Resampling Method for Variable Selection in Robust Regression

Variable selection in regression analysis is of vital importance for data analyst and researcher to fit the parsimonious regression model. With the inundation of large number of predictor variables and large data sets requiring analysis and empirical modeling, contamination becomes usual problem. Accordingly, robust regression estimators are designed to easily fit contaminated data sets. In the last three decades much work have been done regarding various robust regression methods to dealt the data sets contaminated with outliers, relatively less attentions was given to construct a best subset of the predictor variables in robust regression model. We initially considered crossvalidation resampling technique working well for variable selection in linear regression models; see Zafar and Salahuddin (2009, 2011). It turned out that the usual prediction errors inflated by outlier are not the reliable measure for robust model selection. Ultimately, a novel resampling procedure is proposed by introducing alternative and robust prediction error based on Winsor principle in the contaminated model. We demonstrate that superior results for robust model selection are obtainable by relaxing the requirement for the absolute minimum Winsorized prediction error while using our proposed optimum choice of the tuning constant. The simulation study reveals that the proposed technique is working well.