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Robustness of Deepest Regression

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  • Van Aelst, Stefan
  • Rousseeuw, Peter J.

Abstract

In this paper we investigate the robustness properties of the deepest regression, a method for linear regression introduced by Rousseeuw and Hubert [6]. We show that the deepest regression functional is Fisher-consistent for the conditional median, and has a breakdown value of in all dimensions. We also derive its influence function, and compare it with sensitivity functions.

Suggested Citation

  • Van Aelst, Stefan & Rousseeuw, Peter J., 2000. "Robustness of Deepest Regression," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 82-106, April.
    • Handle: RePEc:eee:jmvana:v:73:y:2000:i:1:p:82-106
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    Citations

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    Cited by:

    1. Yijun Zuo, 2020. "Depth Induced Regression Medians and Uniqueness," Stats, MDPI, vol. 3(2), pages 1-13, April.
    2. Zuo, Yijun, 2020. "Large sample properties of the regression depth induced median," Statistics & Probability Letters, Elsevier, vol. 166(C).
    3. Zuo, Yijun, 2021. "Computation of projection regression depth and its induced median," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    4. Mizera, Ivan & Volauf, Milos, 2002. "Continuity of Halfspace Depth Contours and Maximum Depth Estimators: Diagnostics of Depth-Related Methods," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 365-388, November.
    5. Van Aelst, Stefan & Rousseeuw, Peter J. & Hubert, Mia & Struyf, Anja, 2002. "The Deepest Regression Method," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 138-166, April.
    6. Zuo, Yijun, 2024. "Non-asymptotic robustness analysis of regression depth median," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    7. Debruyne, M. & Hubert, M. & Portnoy, S. & Vanden Branden, K., 2008. "Censored depth quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1604-1614, January.
    8. Kris Boudt & Derya Caliskan & Christophe Croux, 2011. "Robust explicit estimators of Weibull parameters," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(2), pages 187-209, March.
    9. Müller, Christine H., 2005. "Depth estimators and tests based on the likelihood principle with application to regression," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 153-181, July.
    10. Yijun Zuo, 2021. "Robustness of the deepest projection regression functional," Statistical Papers, Springer, vol. 62(3), pages 1167-1193, June.

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