An Efficient Algorithm for the MSAE and the MMAE Regression Problems

In the past quarter century, the minimum sum of absolute errors (MSAE) regression and the minimization of the maximum absolute error (MMAE) regression have attracted much attention as alternatives to the popular least squares regression. For the multiple linear regression, the MSAE and the MMAE regression problems can be formulated and solved as linear programming problems. Several efficient special purpose algorithms have been developed for each problem. Thus one needs two different algorithms and two separate computer codes to find the MSAE and the MMAE regression equations. In this paper, we develop an efficient algorithm to solve both problems. The proposed algorithm exploits the special structure of and the similarities between the problems. We illustrate it with a simple numerical example.