An overview of the variables selection methods for the minimum sum of absolute errors regression

The minimum sum of absolute errors regression is a robust alternative to the least squares regression whenever the errors follow a distribution for which the sample median is a more efficient estimator of location parameter than the sample mean, the errors follow a long tailed distribution, there are outliers in the values of the response variable in the data or the absolute error loss function is more appropriate than the quadratic loss function. Often an initial model may contain a large number of variables. However, in many situations, it is neither necessary nor important to include all the variables in the model. The methods for variable selection for the minimum sum of absolute errors regression are not as well documented and known as for the least squares regression. Our objective is to present an overview of the procedures to fit models with fewer variables and some criteria for selecting a model. Copyright (C) 2003 John Wiley Sons, Ltd.