The Shooting S-Estimator for Robust Regression

22 Pages Posted: 22 Jan 2014

See all articles by Viktoria Oellerer

Viktoria Oellerer

KU Leuven - Department of Applied Economics

Andreas Alfons

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE)

Christophe Croux

KU Leuven - Faculty of Business and Economics (FEB)

Date Written: 2013

Abstract

To perform multiple regression, the least squares estimator is commonly used. However, this estimator is not robust to outliers. Therefore, robust methods such as MM-estimation have been proposed. These estimators flag any observation with a large residual as an outlier and downweight it in the further procedure. This is also the case if the large residual is caused by only one component of the observation, which results in a loss of information.

Therefore, we propose the shooting S-estimator, a regression estimator that is especially designed for situations where a large number of observations suffer from contamination in a small number of predictor variables. The shooting S-estimator combines the ideas of the coordinate descent algorithm with simple S-regression, which makes it robust against componentwise contamination.

Keywords: cellwise outliers, componentwise contamination, shooting algorithm, coordinate descent algorithm, regression S-estimation

Suggested Citation

Oellerer, Viktoria and Alfons, Andreas and Croux, Christophe, The Shooting S-Estimator for Robust Regression (2013). Available at SSRN: https://ssrn.com/abstract=2381960 or http://dx.doi.org/10.2139/ssrn.2381960

Viktoria Oellerer (Contact Author)

KU Leuven - Department of Applied Economics ( email )

Leuven, B-3000
BELGIUM

Andreas Alfons

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE) ( email )

P.O. Box 1738
3000 DR Rotterdam, NL 3062 PA
Netherlands

Christophe Croux

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

Naamsestraat 69
Leuven, B-3000
Belgium

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