Sparse least trimmed squares regression for analyzing high-dimensional large data sets
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2013
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| _version_ | 1866910806274211840 |
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| author | Alfons, Andreas Croux, Christophe Gelper, Sarah |
| author_facet | Alfons, Andreas Croux, Christophe Gelper, Sarah |
| contents | 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 $L_1$ 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. In addition, the sparse LTS is applied to protein and gene expression data of the NCI-60 cancer cell panel. Both a simulation study and the real data application show that the sparse LTS has better prediction performance than its competitors in the presence of leverage points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1304_4773 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Sparse least trimmed squares regression for analyzing high-dimensional large data sets Alfons, Andreas Croux, Christophe Gelper, Sarah Applications 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 $L_1$ 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. In addition, the sparse LTS is applied to protein and gene expression data of the NCI-60 cancer cell panel. Both a simulation study and the real data application show that the sparse LTS has better prediction performance than its competitors in the presence of leverage points. |
| title | Sparse least trimmed squares regression for analyzing high-dimensional large data sets |
| topic | Applications |
| url | https://arxiv.org/abs/1304.4773 |