LAD Regression for Detecting Outliers in Response and Explanatory Variables

Least absolute deviations regression resists outliers in the response variable but is relatively sensitive to outlying observations in the explanatory variables. In this paper a simple solution is proposed to overcome this problem. This is achieved by minimizing the absolute values of vertical and horizontal deviations in turn. Two algorithms are proposed: one for the simple and one for the multiple regression case. The methods presented have been tested on a variety of data and have proven to be quite effective.