Constrained M-Estimation for Regression

  • Beatriz Mendes
  • David E. Tyler
Part of the Lecture Notes in Statistics book series (LNS, volume 109)


When using redescending M-estimates of regression, one must choose not only an estimate of scale, but since the redescending M-estimating equations may admit multiple solutions, of which all of them may not be a desired solution, one must also have a method for choosing a desirable solution to the estimating equations. We introduce here a new approach for properly scaling redescending M-estimating equations and for obtaining high breakdown point solutions to the equations by the introduction of the constrained M-estimates of regression, or the CM-estimates of regression for short. Unlike the S-estimates of regression, the CM-estimates of regression can be tuned to obtain good local robustness properties while maintaining a breakdown point of 1/2.

Keywords and phrases

Breakdown point M-estimates robust estimation S-estimates 

AMS 1991 subject classifications

Primary 62F35 secondary 62J05 


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Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • Beatriz Mendes
    • 1
  • David E. Tyler
    • 1
  1. 1.Rutgers UniversityNew BrunswickCanada

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