A robust sparse linear approach for contaminated data

Abstract

A challenging problem in a linear regression model is to select a parsimonious model which is robust to the presence of contamination in the data. In this paper, we present a sparse linear approach which detects outliers by using a highly robust regression method. The model with optimal predictive ability as measured by the median absolute deviation of the prediction errors on JackKnife subsets is used to detect outliers. The performance of the proposed method is evaluated on a simulation study with a different type of outliers and high leverage points and also on a real data set.