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Algorithms to Compute CM- and S-Estimates for Regression

In: Developments in Robust Statistics

Author

Listed:
  • O. Arslan

    (University of Cukurova, Department of Mathematics)

  • O. Edlund

    (Luleå University of Technology, Department of Mathematics)

  • H. Ekblom

    (Luleå University of Technology, Department of Mathematics)

Abstract

Summary Constrained M-estimators for regression were introduced by Mendes and Tyler (1995) as an alternative class of robust regression estimators with high breakdown point and high asymptotic efficiency. To compute the CM-estimate, the global minimum of an objective function with an inequality constraint has to be localized. To find the S-estimate for the same problem, we instead restrict ourselves to the boundary of the feasible region. The algorithm presented for computing CM-estimates can easily be modified to compute S-estimates as well. Testing is carried out with a comparison to the algorithm SURREAL by Ruppert (1992).

Suggested Citation

  • O. Arslan & O. Edlund & H. Ekblom, 2003. "Algorithms to Compute CM- and S-Estimates for Regression," Springer Books, in: Rudolf Dutter & Peter Filzmoser & Ursula Gather & Peter J. Rousseeuw (ed.), Developments in Robust Statistics, pages 62-76, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-57338-5_5
    DOI: 10.1007/978-3-642-57338-5_5
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