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Robustness

  • Roger Koenker
  • Douglas Simpson
Chapter
  • 726 Downloads

Abstract

We are delighted to have the opportunity to introduce Ray’s papers on robustness in statistics. These papers include important breakthrough developments such as the first rigorous asymptotic analysis of trimmed least squares, the first robust heteroscedastic regression estimators, the first efficient bounded-influence estimators for generalized linear regression, and the first bounded-influence regression estimators with high breakdown points. Like so many of Ray’s publications, each of these widely cited papers is a marvel of clarity, innovation, and deep analysis.

Keywords

Rigorous Asymptotic Analysis High Breakdown Point Marvel Deeper Analysis Regression Estimator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

Other publications by Ray Carroll cited in this chapter.

  1. Carroll, R. J., and Pederson, S. (1993). On robustness in the logistic regression model. Journal of the Royal Statistical Society, Series B, 55, 693–706.zbMATHMathSciNetGoogle Scholar
  2. Carroll, R. J., and Welsh, A. H., (1989). A note on asymmetry and robustness in linear regression. The American Statistician, 42, 285–287.MathSciNetGoogle Scholar
  3. Simpson, D. G., Carroll, R. J., and Ruppert, D. (1987). M-estimation for discrete data: asymptotic distribution theory and implications. Annals of Statistics, 15, 657–669.CrossRefzbMATHMathSciNetGoogle Scholar

Publications by other authors cited in this chapter.

  1. Bickel, P. J. (1975). One-step Huber estimates in the linear model. Journal of the American Statistical Association, 70, 428–434.CrossRefzbMATHMathSciNetGoogle Scholar
  2. Hampel, F. R. (1968). Contributions to the theory of robust estimation. Ph.D. Thesis. University of California, Berkeley.Google Scholar
  3. Hampel, F. R., Ronchetti, E. M., Rousseeuw, P.J., and Stahel, W. (1986) Robust Statistics, Wiley: New York.zbMATHGoogle Scholar
  4. He, X., Simpson, D. G., and Wang, G. (2000). Breakdown points of t-type regression estimators. Biometrika, 87, 675–687.CrossRefzbMATHMathSciNetGoogle Scholar
  5. Koenker, R. and Bassett, G., Jr. (1978). Regression quantiles. Econometrica, 46, 33–50.CrossRefzbMATHMathSciNetGoogle Scholar
  6. Krasker, W. S. and Welsch, R. E. (1982). Efficient bounded-influence regression estimation using alternative definitions of sensitivity. Journal of the American Statistical Association, 77, 595–605.CrossRefzbMATHMathSciNetGoogle Scholar
  7. Maronna, R. A., Bustos, O. H., and Yohai, V. J. (1979). Bias- and efficiency-robustness of general M-estimators for regression with random carriers. In Smoothing Techniques for Curve Estimation, eds. T. Gasser and M. Rosenblatt, Springer-Verlag: New York.Google Scholar
  8. Rousseeuw, P. J. (1984). Least median of squares regression. Journal of the American Statistical Association, 79, 871–880.CrossRefzbMATHMathSciNetGoogle Scholar
  9. Rousseeuw, P. J. and van Zomeren, B. C. (1990). Unmasking multivariate outliers and leverage points. Journal of the American Statistical Association, 85, 633–639.CrossRefGoogle Scholar
  10. Simpson, D. G. and Yohai, V. J., (1998). Functional stability of one-step GM-estimators in approximately linear regression. Annals of Statistics, 26, 1147–1169.CrossRefzbMATHMathSciNetGoogle Scholar
  11. Welsh, A. H. (1987). The trimmed mean in the linear model. Annals of Statistics, 15, 20–36.CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Roger Koenker
    • 1
  • Douglas Simpson
    • 1
  1. 1.University of IllinoisUrbana-ChampaignUSA

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