$L_1$ estimation for the simple linear regression model

Abstract

When the error term does not follow the normal distribution in the linear regression model, the least absolute values estimation is considered as one of the alternative methods to the least squares estimation. Many algorithms have been developed to solve the L$_1$ estimation. The direct descent algorithm to solve the overdetermined linear system in the L$_1$ norm can be applied easily to solve the linear regression problem. In this thesis, the direct descent method is modified to solve the simple linear regression problem and the results of the comparison with other algorithms are given.