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Asymptotic Theory For Some High Breakdown Point Estimators

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  • Zinde-Walsh, Victoria

Abstract

High breakdown point estimators in regression are robust against gross contamination in the regressors and also in the errors; the least median of squares (LMS) estimator has the additional property of packing the majority of the sample most tightly around the estimated regression hyperplane in terms of absolute deviations of the residuals and thus is helpful in identifying outliers. Asymptotics for a class of high breakdown point smoothed LMS estimators are derived here under a variety of conditions that allow for time series applications; joint limit processes for several smoothed estimators are examined. The limit process for the LMS estimator is represented via a generalized Gaussian process that defines the generalized derivative of the Wiener process.

Suggested Citation

  • Zinde-Walsh, Victoria, 2002. "Asymptotic Theory For Some High Breakdown Point Estimators," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1172-1196, October.
    • Handle: RePEc:cup:etheor:v:18:y:2002:i:05:p:1172-1196_18
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    Cited by:

    1. Čížek, Pavel, 2008. "General Trimmed Estimation: Robust Approach To Nonlinear And Limited Dependent Variable Models," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1500-1529, December.
    2. Cizek, P., 2007. "General Trimmed Estimation : Robust Approach to Nonlinear and Limited Dependent Variable Models (Replaces DP 2007-1)," Other publications TiSEM eeccf622-dd18-41d4-a2f9-b, Tilburg University, School of Economics and Management.
    3. Jun, Sung Jae & Pinkse, Joris & Wan, Yuanyuan, 2011. "-Consistent robust integration-based estimation," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 828-846, April.
    4. Sunil Sapra, 2003. "High-breakdown point estimation of some regression models," Applied Economics Letters, Taylor & Francis Journals, vol. 10(14), pages 875-878.
    5. Cizek, P., 2009. "Generalized Methods of Trimmed Moments," Discussion Paper 2009-25, Tilburg University, Center for Economic Research.
    6. Preminger, Arie & Franck, Raphael, 2007. "Forecasting exchange rates: A robust regression approach," International Journal of Forecasting, Elsevier, vol. 23(1), pages 71-84.
    7. Hong, Han & Mahajan, Aprajit & Nekipelov, Denis, 2015. "Extremum estimation and numerical derivatives," Journal of Econometrics, Elsevier, vol. 188(1), pages 250-263.
    8. Taisuke Otsu & Myung Hwan Seo, 2014. "Asymptotics for maximum score method under general conditions," STICERD - Econometrics Paper Series 571, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    9. Cizek, P., 2004. "Asymptotics of Least Trimmed Squares Regression," Discussion Paper 2004-72, Tilburg University, Center for Economic Research.
    10. Cizek, P., 2007. "Efficient Robust Estimation of Regression Models (Revision of DP 2006-08)," Discussion Paper 2007-87, Tilburg University, Center for Economic Research.
    11. Kotlyarova, Yulia & Zinde-Walsh, Victoria, 2006. "Non- and semi-parametric estimation in models with unknown smoothness," Economics Letters, Elsevier, vol. 93(3), pages 379-386, December.
    12. repec:cep:stiecm:/2014/571 is not listed on IDEAS
    13. 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.
    14. ZINDE-WALSH, Victoria, 2005. "Kernel Estimation when Density Does Not Exist," Cahiers de recherche 09-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    15. Zinde-Walsh, Victoria, 2008. "Kernel Estimation When Density May Not Exist," Econometric Theory, Cambridge University Press, vol. 24(3), pages 696-725, June.
    16. Francisco Alvarez-Cuadrado, 2006. "Improving The Efficiency And Robustness Of The Smoothed Maximum Score Estimator," Departmental Working Papers 2004-01, McGill University, Department of Economics.
    17. Yulia Kotlyarova & Victoria Zinde-Walsh, 2006. "Robust Kernel Estimator For Densities Of Unknown," Departmental Working Papers 2005-05, McGill University, Department of Economics.
    18. Jun, Sung Jae & Pinkse, Joris & Wan, Yuanyuan, 2015. "Classical Laplace estimation for n3-consistent estimators: Improved convergence rates and rate-adaptive inference," Journal of Econometrics, Elsevier, vol. 187(1), pages 201-216.

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