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dc.contributor.authorGong, Z.
dc.contributor.authorLiu, C.
dc.contributor.authorSun, Jie
dc.contributor.authorTeo, Kok Lay
dc.identifier.citationGong, Z. and Liu, C. and Sun, J. and Teo, K.L. 2018. Distributionally robust L1-estimation in multiple linear regression. Optimization Letters. 13 (4): pp. 935-947.

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.

dc.publisherSpringer Verlag
dc.titleDistributionally robust L1-estimation in multiple linear regression
dc.typeJournal Article
dcterms.source.titleOptimization Letters
curtin.departmentSchool of Electrical Engineering, Computing and Mathematical Science (EECMS)
curtin.accessStatusOpen access

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