AN ALTERNATIVE APPROACH TO SOLVE THE LAD-LASSO PROBLEM

Abstract

The least absolute deviation (LAD) regression is more robust alternative to the popular least squares (LS) regression whenever there are outliers in the response variable, or the errors follow a heavy-tailed distribution. The least absolute shrinkage and selection operator (LASSO) is a popular choice for shrinkage estimation and variable selection. By combining these two classical ideas, LAD-LASSO is an estimator which is able to perform shrinkage estimation while at the same time selecting the variables and is resistant to heavy-tailed distributions and outliers. The aim of this article is to reformulate LAD-LASSO problem to solve with the Simplex Algorithm, which is an area of Mathematical Programming.