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High finite-sample efficiency and robustness based on distance-constrained maximum likelihood

Author

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  • Maronna, Ricardo A.
  • Yohai, Victor J.

Abstract

Good robust estimators can be tuned to combine a high breakdown point and a specified asymptotic efficiency at a central model. This happens in regression with MM- and τ-estimators among others. However, the finite-sample efficiency of these estimators can be much lower than the asymptotic one. To overcome this drawback, an approach is proposed for parametric models, which is based on a distance between parameters. Given a robust estimator, the proposed one is obtained by maximizing the likelihood under the constraint that the distance is less than a given threshold. For the linear model with normal errors, simulations show that the proposed estimator attains a finite-sample efficiency close to one while improving the robustness of the initial estimator. The same approach also shows good results in the estimation of multivariate location and scatter.

Suggested Citation

  • Maronna, Ricardo A. & Yohai, Victor J., 2015. "High finite-sample efficiency and robustness based on distance-constrained maximum likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 262-274.
    • Handle: RePEc:eee:csdana:v:83:y:2015:i:c:p:262-274
    DOI: 10.1016/j.csda.2014.10.015
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    References listed on IDEAS

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    1. Howard D. Bondell & Leonard A. Stefanski, 2013. "Efficient Robust Regression via Two-Stage Generalized Empirical Likelihood," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 644-655, June.
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    Cited by:

    1. Alfio Marazzi, 2021. "Improving the Efficiency of Robust Estimators for the Generalized Linear Model," Stats, MDPI, vol. 4(1), pages 1-20, February.
    2. Smucler, Ezequiel & Yohai, Victor J., 2017. "Robust and sparse estimators for linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 116-130.

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