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Robust and efficient estimation of the residual scale in linear regression

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  • Van Aelst, Stefan
  • Willems, Gert
  • Zamar, Ruben H.

Abstract

Robustness and efficiency of the residual scale estimators in the regression model is important for robust inference. We introduce the class of robust generalized M-scale estimators for the regression model, derive their influence function and gross-error sensitivity, and study their maxbias behavior. In particular, we find overall minimax bias estimates for the general class and also for well-known subclasses. We pose and solve a Hampel’s-like optimality problem: we find generalized M-scale estimators with maximal efficiency subject to a lower bound on the global and local robustness of the estimators.

Suggested Citation

  • Van Aelst, Stefan & Willems, Gert & Zamar, Ruben H., 2013. "Robust and efficient estimation of the residual scale in linear regression," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 278-296.
    • Handle: RePEc:eee:jmvana:v:116:y:2013:i:c:p:278-296
    DOI: 10.1016/j.jmva.2012.12.008
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    References listed on IDEAS

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    1. Randal, John A., 2008. "A reinvestigation of robust scale estimation in finite samples," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 5014-5021, July.
    2. Van Aelst, Stefan & Willems, Gert, 2011. "Robust and Efficient One-Way MANOVA Tests," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 706-718.
    3. Croux, Christophe & Haesbroeck, Gentiane, 1999. "Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 161-190, November.
    4. Croux, Christophe, 1994. "Efficient high-breakdown M-estimators of scale," Statistics & Probability Letters, Elsevier, vol. 19(5), pages 371-379, April.
    5. Agulló, Jose & Croux, Christophe & Van Aelst, Stefan, 2008. "The multivariate least-trimmed squares estimator," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 311-338, March.
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    Cited by:

    1. Salibian-Barrera, Matias & Van Aelst, Stefan & Yohai, Víctor J., 2016. "Robust tests for linear regression models based on τ-estimates," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 436-455.
    2. Peremans, Kris & Van Aelst, Stefan, 2018. "Robust inference for seemingly unrelated regression models," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 212-224.

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