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A local breakdown property of robust tests in linear regression


  • He, Xuming


The breakdown slope, as a useful summary measure of local stability for estimators and test statistics, has been studied recently by He, Simpson, and Protnoy (1990, J. Amer. Statist. Assoc., 85). It is shown here that all regression estimates based on residuals alone in linear models have zero breakdown slopes in contamination neighborhoods, even though they can have breakdown points as high as one-half. The breakdown functions of tests based on the S-estimation are investigated. It is also shown that the Generalized M-estimators can have better local breakdown robustness. One way to obtain regression estimators with desirable local and global breakdown properties is discussed.

Suggested Citation

  • He, Xuming, 1991. "A local breakdown property of robust tests in linear regression," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 294-305, August.
  • Handle: RePEc:eee:jmvana:v:38:y:1991:i:2:p:294-305

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    Cited by:

    1. Preminger, Arie & Franck, Raphael, 2007. "Forecasting exchange rates: A robust regression approach," International Journal of Forecasting, Elsevier, vol. 23(1), pages 71-84.
    2. Marc G. Genton & André Lucas, 2003. "Comprehensive definitions of breakdown points for independent and dependent observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 81-94.
    3. Gervini, Daniel, 2003. "A robust and efficient adaptive reweighted estimator of multivariate location and scatter," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 116-144, January.
    4. Olive, David J., 2005. "Two simple resistant regression estimators," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 809-819, June.
    5. Agostinelli, Claudio & Markatou, Marianthi, 1998. "A one-step robust estimator for regression based on the weighted likelihood reweighting scheme," Statistics & Probability Letters, Elsevier, vol. 37(4), pages 341-350, March.
    6. Ando, Masakazu & Kimura, Miyoshi, 2004. "The maximum asymptotic bias of S-estimates for regression over the neighborhoods defined by certain special capacities," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 407-425, August.
    7. Sakata, Shinichi & White, Halbert, 2001. "S-estimation of nonlinear regression models with dependent and heterogeneous observations," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 5-72, July.
    8. Olive, David J. & Hawkins, Douglas M., 2003. "Robust regression with high coverage," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 259-266, July.
    9. Olive, David J., 2004. "A resistant estimator of multivariate location and dispersion," Computational Statistics & Data Analysis, Elsevier, vol. 46(1), pages 93-102, May.


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