Least absolute error regression
Date
1998
Authors
Tung, Yi-Yuan
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Abstract
Regression analysis is usually based on the method of least squares . However, the least squares estimator is highly sensitive to outliers and can be far from optimal when the errors are non-normal in distribution. As an alternative to the least squares estimator, the least absolute error estimator has attracted much attention during the past thirty years with the development of several efficient algorithms based on its connections to linear programming, least absolute error regression can be put into practical use.
In this thesis, we review some basic theoretical properties of least absolute error regression, examine the asymptotic efficiency of the least absolute error estimator relative to the least squares estimator for a general family of error distribution, and demonstrate its use for practical data analysis in a variety of situations using computer routines written in S-Plus .