On least absolute values estimation

The resistance of least absolute values (L1) estimators to outliers and their robustness to heavy-tailed distributions make these estimators useful alternatives to the usual least squares estimators. The recent development of efficient algorithms for L1 estimation in linear models has permitted their use in practical data analysis. Although in general the L1 estimators are not unique, there are a number of properties they all share. The set of all L1 estimators for a given model and data set can be characterized as the convex hull of some extreme estimators. Properties of the extreme estimators and of the L1-estimate set are considered.