Robust and high-breakdown fits of polynomial models

Joseph W. McKean, Simon J. Sheather, Thomas P. Hettmansperger

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


A common strategy for fitting a polynomial regression model is to use a combination of residual plots and significance tests on the regression coefficients. In this article, we consider whether this strategy can be used effectively for fits based on two classes of robust estimatesnamely—M estimates and GM estimates. We show that the asymptotic relative efficiency of Mallows-type high-breakdown GM estimates can be quite low for detecting curvature in polynomial models. Furthermore, the GM-residual plots may also be of little help in detecting curvature. An example and a simulation study illustrate the discussion.

Original languageEnglish
Pages (from-to)409-415
Number of pages7
Issue number4
StatePublished - Nov 1994

Bibliographical note

Funding Information:
The work of Joseph W. McKean was partially supported by National Science Foundation Grant DMS-9103916,t he work of Simon J. Sheather was partially supported by the Australian Research Council, and the work of Thomas P. Hettmansperger was partially supported by National Science Foundation Grant DMS-9100228 AOl. We thank anonymous referees for helpful comments on an earlier version of this article.


  • GM estimate
  • Linear model
  • M estimate
  • Residual plot
  • Robust

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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