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Robust weighted orthogonal regression in the errors-in-variables model

Author

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  • Fekri, M.
  • Ruiz-Gazen, A.

Abstract

This paper focuses on robust estimation in the structural errors-in-variables (EV) model. A new class of robust estimators, called weighted orthogonal regression estimators, is introduced. Robust estimators of the parameters of the EV model are simply derived from robust estimators of multivariate location and scatter such as the M-estimators, the S-estimators and the MCD estimator. The influence functions of the proposed estimators are calculated and shown to be bounded. Moreover, we derive the asymptotic distributions of the estimators and illustrate the results on simulated examples and on a real-data set.

Suggested Citation

  • Fekri, M. & Ruiz-Gazen, A., 2004. "Robust weighted orthogonal regression in the errors-in-variables model," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 89-108, January.
    • Handle: RePEc:eee:jmvana:v:88:y:2004:i:1:p:89-108
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    References listed on IDEAS

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    1. R. Ketellapper & A. Ronner, 1984. "Are robust estimation methods useful in the structural errors-in-variables model?," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 31(1), pages 33-41, December.
    2. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
    3. Maronna, Ricardo A. & Stahel, Werner A. & Yohai, Victor J., 1992. "Bias-robust estimators of multivariate scatter based on projections," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 141-161, July.
    4. 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.
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    Cited by:

    1. Fekri, M. & Ruiz-Gazen, A., 2006. "Robust estimation in the simple errors-in-variables model," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1741-1747, October.
    2. Cator, Eric A. & Lopuhaä, Hendrik P., 2010. "Asymptotic expansion of the minimum covariance determinant estimators," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2372-2388, November.
    3. Eric Blankmeyer, 2018. "Measurement Errors as Bad Leverage Points," Papers 1807.02814, arXiv.org, revised Mar 2020.
    4. Bianco, Ana M. & Spano, Paula M., 2017. "Robust estimation in partially linear errors-in-variables models," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 46-64.
    5. Kang-Mo Jung, 2007. "Least Trimmed Squares Estimator in the Errors-in-Variables Model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(3), pages 331-338.

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