MAXIMUM LIKELIHOOD APPROACH TO LEAST ABSOLUTE DEVIATION REGRESSION

Abstract

Least Absolute Deviation (LAD) regression is an important tool used in numerous applications throughout science and engineering, mainly due to the intrinsic robust characteristics of LAD. In this chapter, we show that the optimization needed to solve the LAD regression problem can be viewed as a sequence of Maximum Likelihood Estimates (MLE) of location. Requiring weighted medians only, the new algorithm can be easily modularized for hardware implementation, as opposed to most of the other existing LAD methods which require complicated operations suchas matrix entry manipulations. Simulation shows that the new algorithm is superior in speed to Wesolowsky"s algorithm, which is simple in structure as well. In this paper, Maximum likelihood approach to least absolute deviation regression were discussed