On least absolute values estimation
- 1 January 1977
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics - Theory and Methods
- Vol. 6 (9) , 839-845
- https://doi.org/10.1080/03610927708827535
Abstract
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.Keywords
This publication has 2 references indexed in Scilit:
- On L1 and Chebyshev estimationMathematical Programming, 1973
- An Improved Algorithm for Discrete $l_1 $ Linear ApproximationSIAM Journal on Numerical Analysis, 1973