Perturbation analysis for the minimum sum of absolute errors regression

Abstract

In this paper we study the effect of independent and simultaneous changes in the values of the response variable for all the observations on the minimum sum of absolute errors (or for brevity absolute errors) regression. We develop an algorithm to determine the maximum amount by which the values of the response variable can change without changing the absolute errors regression hyperplane. We illustrate the results with an example.

Keywords:

• L1-norm
• Least absolute value
• Outlier,
• Sensitivity analysis
• Tolerance approach

^∗Current Address: AT&T Bell Laboratories, Holmdel, New Jersey, 07733, USA.

^∗Current Address: AT&T Bell Laboratories, Holmdel, New Jersey, 07733, USA.

Notes

^∗Current Address: AT&T Bell Laboratories, Holmdel, New Jersey, 07733, USA.