The use and interpretation of residuals based on Robust estimation

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

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


Residual plots and diagnostic techniques are important tools for examining the fit of a regression model. In the case of least squares fits, plots of residuals provide a visual assessment of the adequacy of various aspects of the fitted model. An important question is whether plots of robust residuals can be interpreted in the same manner as their least squares counterparts. This article addresses this problem for two popular classes of robust estimates: M estimates and GM estimates of the Mallows and Schweppe types. First-order properties of the residuals and fitted values are derived under correct and misspecified models. These properties are insightful on the general interpretability of robust residual plots and on their ability to detect curvature in misspecified models. The results of a simulation study consisting of tests for randomness and curvature in residual plots supports these theoretical properties. Standardization of robust residuals is also presented.

Original languageEnglish
Pages (from-to)1254-1263
Number of pages10
JournalJournal of the American Statistical Association
Issue number424
StatePublished - Dec 1993

Bibliographical note

Funding Information:
* Joseph W. McKean is Professor of Statistics, Depktment of Mathematics and Statistics, Western Michigan University, Kalamazoo, MI 49008. Simon J. Sheather is Senior Lecturer, Australian Graduate School of Management, University of New South Wales, Kensington, NSW, 2033, Australia. Thomas P. Hettmansperger is Professor of Statistics, Department of Statistics, Penn- sylvania State University, University Park, PA 16802. McKean’s research was partially supported by National Science Foundation Grant DMS- 9 1039 16; Sheather’s research was partially supported by grant support from the Australian Research Council; and Hettmansperger’s research was partially supported by National Science Foundation Grant DMS-9100228 AOI. The authors thank the referees for helpful comments on an earlier version of this article.


  • GM estimate
  • High breakdown
  • Linear model
  • M estimate
  • Regression diagnostic
  • Residual plot

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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