The shooting S-estimator for robust regression
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2015
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| author | Öllerer, Viktoria Alfons, Andreas Croux, Christophe |
| author_facet | Öllerer, Viktoria Alfons, Andreas Croux, Christophe |
| contents | To perform multiple regression, the least squares estimator is commonly used. However, this estimator is not robust to outliers. Therefore, robust methods such as S-estimation have been proposed. These estimators flag any observation with a large residual as an outlier and downweight it in the further procedure. However, a large residual may be caused by an outlier in only one single predictor variable, and downweighting the complete observation 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, at the cost of failing the regression equivariance property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1506_01223 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | The shooting S-estimator for robust regression Öllerer, Viktoria Alfons, Andreas Croux, Christophe Methodology To perform multiple regression, the least squares estimator is commonly used. However, this estimator is not robust to outliers. Therefore, robust methods such as S-estimation have been proposed. These estimators flag any observation with a large residual as an outlier and downweight it in the further procedure. However, a large residual may be caused by an outlier in only one single predictor variable, and downweighting the complete observation 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, at the cost of failing the regression equivariance property. |
| title | The shooting S-estimator for robust regression |
| topic | Methodology |
| url | https://arxiv.org/abs/1506.01223 |