The minimum sum of absolute errors regression: a robust alternative to the least squares regression

Abstract

This paper concerns the minimum sum of absolute errors regression. It is a more robust alternative to the popular least squares regression whenever there are outliers in the values of the response variable, or the errors follow a long tailed distribution, or the loss function is proportional to the absolute errors rather than their squared values. We use data from a study of interstitial lung disease to illustrate the method, interpret the findings, and contrast with least squares regression. We point out some of the problems with the least squares analysis and show how to avoid these with the minimum sum of absolute errors analysis.