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The least trimmed quantile regression

Author

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  • Neykov, N.M.
  • Čížek, P.
  • Filzmoser, P.
  • Neytchev, P.N.

Abstract

The linear quantile regression estimator is very popular and widely used. It is also well known that this estimator can be very sensitive to outliers in the explanatory variables. In order to overcome this disadvantage, the usage of the least trimmed quantile regression estimator is proposed to estimate the unknown parameters in a robust way. As a prominent measure of robustness, the breakdown point of this estimator is characterized and its consistency is proved. The performance of this approach in comparison with the classical one is illustrated by an example and simulation studies.

Suggested Citation

  • Neykov, N.M. & Čížek, P. & Filzmoser, P. & Neytchev, P.N., 2012. "The least trimmed quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1757-1770.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1757-1770
    DOI: 10.1016/j.csda.2011.10.023
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    References listed on IDEAS

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    Cited by:

    1. G. Zioutas & C. Chatzinakos & T. D. Nguyen & L. Pitsoulis, 2017. "Optimization techniques for multivariate least trimmed absolute deviation estimation," Journal of Combinatorial Optimization, Springer, vol. 34(3), pages 781-797, October.
    2. Umberto Nizza, 2023. "The expertise effect: the impact of legal specialists’ intervention on the timely delivery of laymen's judgments," Economia Politica: Journal of Analytical and Institutional Economics, Springer;Fondazione Edison, vol. 40(2), pages 589-614, July.
    3. Mafusalov, Alexander & Uryasev, Stan, 2016. "CVaR (superquantile) norm: Stochastic case," European Journal of Operational Research, Elsevier, vol. 249(1), pages 200-208.
    4. N. Neykov & P. Filzmoser & P. Neytchev, 2014. "Ultrahigh dimensional variable selection through the penalized maximum trimmed likelihood estimator," Statistical Papers, Springer, vol. 55(1), pages 187-207, February.
    5. Yu-Yen Ku & Tze-Yu Yen, 2016. "Heterogeneous Effect of Financial Leverage on Corporate Performance: A Quantile Regression Analysis of Taiwanese Companies," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-33, September.

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