Outlier detection and variable selection via difference based regression model and penalized regression

Abstract

This paper studies an efficient procedure for the outlier detection and variable selection problem in linear regression. The effect of outliers is added in linear regression as a mean shift parameter, nonzero or zero constant. To t this mean shift model, most penalized regressions have used some adaptive penalties on the parameters to shrink most of the parameters to zero. Such penalized models do select the true variables well, but do not detect the outliers correctly. To overcome this problem, we first determine a group of possibly suspected outliers using difference-based regression model (DBRM) and add the group to the linear model as the parameters of the effect of each suspected outlier. Then, we perform outlier detection and variable selection simultaneously using Lasso regression or Elastic net regression for the linear regression with the effect term of each suspected outlier added. The proposed method is more efficient than the previous penalized regression. We compare the proposed procedure with other methods using a simulation study and apply this procedure to the real data.