Multivariate multiple linear regression based on the minimum sum of absolute errors criterion

Abstract

We propose the minimum sum of absolute errors (MSAE) criterion for estimating the unknown parameters of a multivariate multiple linear regression model. It is less sensitive to outliers than the popular least squares procedure. A multivariate multiple linear regression problem may be viewed as a multiple criteria decision problem. Using the MSAE criterion the estimation problem can be formulated and solved as a multiple objective linear programming problem. We illustrate the idea with a bicriteria example.