Name
Abstract | ||
|---|---|---|
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 \(L_1\)-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. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1007/s11590-018-1299-x | Optimization Letters |
Keywords | DocType | Volume |
Multiple linear regression, Least absolute value estimation, Conic optimization, Semi-infinite optimization | Journal | 13.0 |
Issue | ISSN | Citations |
4.0 | 1862-4480 | 1 |
PageRank | References | Authors |
0.37 | 8 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zhaohua Gong | 1 | 22 | 5.31 |
| Chongyang Liu | 2 | 17 | 4.02 |
| Jie Sun | 3 | 1303 | 113.30 |
| K. L. Teo | 4 | 1643 | 211.47 |