A fast maximum likelihood estimation approach to LAD regression

In this paper, we show that the optimization needed to solve the least absolute deviations (LAD) regression problem can be viewed as a sequence of maximum likelihood estimates (MLE) of location. The derived algorithm reduces to an iterative procedure where a simple coordinate transformation is applied during each iteration to direct the optimization procedure along edge lines of the cost surface, followed by a MLE estimate of location which is executed by a weighted median operation. 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 such as matrix entry manipulations. The new algorithm provides a better trade-off solution between convergence speed and implementation complexity compared to existing algorithms.