Robust Variable Selection Based on Schwarz Information Criterion for Linear Regression Models

Abstract

Schwarz information criterion (SIC) is a popular tool to select the best variables in regression data sets. However, SIC defined using an unbounded estimator (Least Squares (LS)) which is very sensitive to the presence of outlying observations, especially bad leverage points. Thus, robust variable selection based on SIC for linear regression models is in need. This paper study the robust properties of SIC derives its influence function and proposes robust SIC based on the MM-estimation scale, aim to produce criterion which is effective in selecting accurate models in the presence of vertical outliers and high leverage points. The advantages of the proposed robust SIC is demonstrated through simulation study and analysis of a real data set.