Distributionally robust L1-estimation in multiple linear regression
Linear regression is one of the most important and widely used techniques in data analysis, for which a key step is the estimation of the unknown parameters. However, it is often carried out under the assumption that the full information of the error distribution is available. This is clearly unreal...
| Main Authors: | , , , |
|---|---|
| Format: | Journal Article |
| Published: |
Springer Verlag
2018
|
| Online Access: | http://purl.org/au-research/grants/arc/DP160102819 http://hdl.handle.net/20.500.11937/73292 |
| _version_ | 1848762975716900864 |
|---|---|
| author | Gong, Z. Liu, C. Sun, Jie Teo, Kok Lay |
| author_facet | Gong, Z. Liu, C. Sun, Jie Teo, Kok Lay |
| author_sort | Gong, Z. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Linear regression is one of the most important and widely used techniques in data analysis, for which a key step is the estimation of the unknown parameters. However, it is often carried out under the assumption that the full information of the error distribution is available. This is clearly unrealistic in practice. In this paper, we propose a distributionally robust formulation of L1-estimation (or the least absolute value estimation) problem, where the only knowledge on the error distribution is that it belongs to a well-defined ambiguity set. We then reformulate the estimation problem as a computationally tractable conic optimization problem by using duality theory. Finally, a numerical example is solved as a conic optimization problem to demonstrate the effectiveness of the proposed approach. |
| first_indexed | 2025-11-14T10:56:07Z |
| format | Journal Article |
| id | curtin-20.500.11937-73292 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:56:07Z |
| publishDate | 2018 |
| publisher | Springer Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-732922022-10-27T04:49:04Z Distributionally robust L1-estimation in multiple linear regression Gong, Z. Liu, C. Sun, Jie Teo, Kok Lay Linear regression is one of the most important and widely used techniques in data analysis, for which a key step is the estimation of the unknown parameters. However, it is often carried out under the assumption that the full information of the error distribution is available. This is clearly unrealistic in practice. In this paper, we propose a distributionally robust formulation of L1-estimation (or the least absolute value estimation) problem, where the only knowledge on the error distribution is that it belongs to a well-defined ambiguity set. We then reformulate the estimation problem as a computationally tractable conic optimization problem by using duality theory. Finally, a numerical example is solved as a conic optimization problem to demonstrate the effectiveness of the proposed approach. 2018 Journal Article http://hdl.handle.net/20.500.11937/73292 10.1007/s11590-018-1299-x http://purl.org/au-research/grants/arc/DP160102819 http://purl.org/au-research/grants/arc/DP140100289 Springer Verlag fulltext |
| spellingShingle | Gong, Z. Liu, C. Sun, Jie Teo, Kok Lay Distributionally robust L1-estimation in multiple linear regression |
| title | Distributionally robust L1-estimation in multiple linear regression |
| title_full | Distributionally robust L1-estimation in multiple linear regression |
| title_fullStr | Distributionally robust L1-estimation in multiple linear regression |
| title_full_unstemmed | Distributionally robust L1-estimation in multiple linear regression |
| title_short | Distributionally robust L1-estimation in multiple linear regression |
| title_sort | distributionally robust l1-estimation in multiple linear regression |
| url | http://purl.org/au-research/grants/arc/DP160102819 http://purl.org/au-research/grants/arc/DP160102819 http://hdl.handle.net/20.500.11937/73292 |