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Locally and globally robust estimators in regression

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  • Hernández, Sonia
  • Yohai, Víctor J.

Abstract

A new class of estimates for the linear model is introduced. These estimators, that we eaU C-estimators, are defined as a linear convex combination of the Rousseeuw's least median squares (LMS-) estimator and any other estimate, T2• We prove that C-estimators retain the high breakdown point of the LMS-estimator, but inherit the asymptotic properties and the behaviour in terms of local robutness of T2• In particular, a Cestimators will have --In-asymptotics and bounded contamination sensitivity if T2 does. In addition, efficiency, local robustness properties and the maximum bias curve of C-estimators are investigated for different choices ofT2•

Suggested Citation

  • Hernández, Sonia & Yohai, Víctor J., 1999. "Locally and globally robust estimators in regression," DES - Working Papers. Statistics and Econometrics. WS 6348, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:6348
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    References listed on IDEAS

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    1. 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.
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    Keywords

    Linear regression;

    Statistics

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