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Robust Standard Errors for Robust Estimators


  • Christophe Croux
  • Geert Dhaene
  • Dirk Hoorelbeke


A regression estimator is said to be robust if it is still reliable in the presence of outliers. On the other hand, its standard error is said to be robust if it is still reliable when the regression errors are autocorrelated and/or heteroskedastic. This paper shows how robust standard errors can be computed for several robust estimators of regression, including MMestimators. The improvement relative to non-robust standard errors is illustrated by means of large-sample bias calculations, simulations, and a real data example. It turns out that non-robust standard errors of robust estimators may be severely biased. However, if autocorrelation and heteroscedasticity are absent, non-robust standard errors are more e.cient than the robust standard errors that we propose. We therefore also present a test of the hypothesis that the robust and non-robust standard errors have the same probability limit.

Suggested Citation

  • Christophe Croux & Geert Dhaene & Dirk Hoorelbeke, 2003. "Robust Standard Errors for Robust Estimators," Working Papers Department of Economics ces0316, KU Leuven, Faculty of Economics and Business, Department of Economics.
  • Handle: RePEc:ete:ceswps:ces0316

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    Cited by:

    1. Robert Finger, 2010. "Revisiting the Evaluation of Robust Regression Techniques for Crop Yield Data Detrending," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 92(1), pages 205-211.
    2. Hagen, Tobias, 2013. "Impact of national financial regulation on macroeconomic and fiscal performance after the 2007 financial shock: Econometric analyses based on cross-country data," Economics Discussion Papers 2013-26, Kiel Institute for the World Economy (IfW).
    3. Hagen, Tobias, 2013. "Impact of national financial regulation on macroeconomic and fiscal performance after the 2007 financial stock: Econometric analyses based on cross-country data," Working Paper Series: Business and Law 02, Frankfurt University of Applied Sciences, Faculty of Business and Law.
    4. Andreas Alfons & Wolfgang Baaske & Peter Filzmoser & Wolfgang Mader & Roland Wieser, 2011. "Robust variable selection with application to quality of life research," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(1), pages 65-82, March.
    5. Matías Salibián-Barrera & Stefan Aelst & Gert Willems, 2008. "Fast and robust bootstrap," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(1), pages 41-71, February.
    6. Catherine Dehon & Marjorie Gassner & Vincenzo Verardi, 2011. "Extending the Hausman Test to Check for the presence of Outliers," Working Papers ECARES ECARES 2011-036, ULB -- Universite Libre de Bruxelles.
    7. Marek Omelka & Matías Salibián-Barrera, 2010. "Uniform asymptotics for S- and MM-regression estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(5), pages 897-927, October.
    8. Rodolphe Desbordes & Vincenzo Verardi, 2011. "The Positive Causal Impact of Foreign Direct Investment on Productivity: A Not So Typical Relationship," Working Papers 1106, University of Strathclyde Business School, Department of Economics.

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    robust regression; robust standard errors; autocorrelation; heteroskedasticity;

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