Sparse Least Trimmed Squares Regression

21 Pages Posted: 3 Dec 2011

See all articles by Andreas Alfons

Andreas Alfons

Katholieke Universiteit Leuven - Faculty of Business and Economics (FBE)

Christophe Croux

KU Leuven - Faculty of Business and Economics (FEB)

Sarah Gelper

KU Leuven - Faculty of Business and Economics (FEB)

Date Written: 2011

Abstract

Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the data. This paper combines robust regression and sparse model estimation. A robust and sparse estimator is introduced by adding an L1 penalty on the coefficient estimates to the well known least trimmed squares (LTS) estimator. The breakdown point of this sparse LTS estimator is derived, and a fast algorithm for its computation is proposed. Both the simulation study and the real data example show that the LTS has better pre- diction performance than its competitors in the presence of leverage points.

Keywords: breakdown point, outliers, penalized regression, robust regression, trimming

Suggested Citation

Alfons, Andreas and Croux, Christophe and Gelper, Sarah, Sparse Least Trimmed Squares Regression (2011). Available at SSRN: https://ssrn.com/abstract=1967418 or http://dx.doi.org/10.2139/ssrn.1967418

Andreas Alfons (Contact Author)

Katholieke Universiteit Leuven - Faculty of Business and Economics (FBE) ( email )

Naamsestraat 69
Leuven, B-3000
Belgium

Christophe Croux

KU Leuven - Faculty of Business and Economics (FEB) ( email )

Naamsestraat 69
Leuven, B-3000
Belgium

Sarah Gelper

KU Leuven - Faculty of Business and Economics (FEB) ( email )

Naamsestraat 69
Leuven, B-3000
Belgium

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