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Efficient Robust Regression via Two-Stage Generalized Empirical Likelihood

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  • Howard D. Bondell
  • Leonard A. Stefanski

Abstract

Large- and finite-sample efficiency and resistance to outliers are the key goals of robust statistics. Although often not simultaneously attainable, we develop and study a linear regression estimator that comes close. Efficiency is obtained from the estimator's close connection to generalized empirical likelihood, and its favorable robustness properties are obtained by constraining the associated sum of (weighted) squared residuals. We prove maximum attainable finite-sample replacement breakdown point and full asymptotic efficiency for normal errors. Simulation evidence shows that compared to existing robust regression estimators, the new estimator has relatively high efficiency for small sample sizes and comparable outlier resistance. The estimator is further illustrated and compared to existing methods via application to a real dataset with purported outliers.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:502:p:644-655
    DOI: 10.1080/01621459.2013.779847
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    Cited by:

    1. Ronchetti, Elvezio, 2020. "Accurate and robust inference," Econometrics and Statistics, Elsevier, vol. 14(C), pages 74-88.
    2. Jiang, Depeng & Zhao, Puying & Tang, Niansheng, 2016. "A propensity score adjustment method for regression models with nonignorable missing covariates," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 98-119.
    3. Alfio Marazzi, 2021. "Improving the Efficiency of Robust Estimators for the Generalized Linear Model," Stats, MDPI, vol. 4(1), pages 1-20, February.
    4. Masayuki Hirukawa & Mari Sakudo, 2016. "Testing Symmetry of Unknown Densities via Smoothing with the Generalized Gamma Kernels," Econometrics, MDPI, vol. 4(2), pages 1-27, June.
    5. 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.

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