The Linear l1 Estimator and the Huber M-Estimator

@article{Li1998TheLL,
  title={The Linear l1 Estimator and the Huber M-Estimator},
  author={Wu Li and John Swetits},
  journal={SIAM Journal on Optimization},
  year={1998},
  volume={8},
  pages={457-475}
}
Relationships between a linear `1 estimation problem and the Huber M-estimator problem can be easily established by their dual formulations. The least norm solution of a linear programming problem studied by Mangasarian and Meyer [SIAM J. Control Optim., 17 (1979), pp. 745–752] provides a key link between the dual problems. Based on the dual formulations, we establish a local linearity property of the Huber M-estimators with respect to the tuning parameter γ and prove that the solution set of… CONTINUE READING
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