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Duality in robust linear regression using Huber's M-estimator

✍ Scribed by M.Ç. Pinar

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
353 KB
Volume
10
Category
Article
ISSN
0893-9659

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✦ Synopsis

The robust linear regression problem using Huber's piecewise-quadratic M-estimator function is considered. Without exception, computational algorithms for this problem have been primal in nature. In this note, a dual formulation of this problem is derived using Lagrangean duality. It is shown that the dual problem is a strictly convex separable quadratic minimization problem with linear equality and box constraints. Furthermore, the primal solution (Huber's M-estimate) is obtained as the optimal values of the Lagrange multipliers associated with the dual problem. As a result, Huber's M-estimate can be computed using off-the-shelf optimization software.

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