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The least trimmed quantile regression

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Author Info

  • 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.

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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 56 (2012)
Issue (Month): 6 ()
Pages: 1757-1770

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Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1757-1770

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Web page: http://www.elsevier.com/locate/csda

Related research

Keywords: Linear regression; Quantile regression; Least trimmed quantile regression; Breakdown point; Outlier detection;

References

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  1. Tableman, Mara, 1994. "The asymptotics of the least trimmed absolute deviations (LTAD) estimator," Statistics & Probability Letters, Elsevier, vol. 19(5), pages 387-398, April.
  2. Cizek, P., 2004. "General Trimmed Estimation: Robust Approach to Nonlinear and Limited Dependent Variable Models," Discussion Paper 2004-130, Tilburg University, Center for Economic Research.
  3. Neykov, N.M. & Filzmoser, P. & Neytchev, P.N., 2012. "Robust joint modeling of mean and dispersion through trimming," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 34-48, January.
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  5. He, Xuming, et al, 1990. "Tail Behavior of Regression Estimators and Their Breakdown Points," Econometrica, Econometric Society, vol. 58(5), pages 1195-1214, September.
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  7. Jurecková, Jana, 2010. "Finite-sample distribution of regression quantiles," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1940-1946, December.
  8. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, October.
  9. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  10. Tableman, Mara, 1994. "The influence functions for the least trimmed squares and the least trimmed absolute deviations estimators," Statistics & Probability Letters, Elsevier, vol. 19(4), pages 329-337, March.
  11. Hawkins, Douglas M. & Olive, David, 1999. "Applications and algorithms for least trimmed sum of absolute deviations regression," Computational Statistics & Data Analysis, Elsevier, vol. 32(2), pages 119-134, December.
  12. Giloni, Avi & Simonoff, Jeffrey S. & Sengupta, Bhaskar, 2006. "Robust weighted LAD regression," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3124-3140, July.
  13. Van Aelst, Stefan & Rousseeuw, Peter J. & Hubert, Mia & Struyf, Anja, 2002. "The Deepest Regression Method," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 138-166, April.
  14. Vandev, D., 1993. "A note on the breakdown point of the least median of squares and least trimmed squares estimators," Statistics & Probability Letters, Elsevier, vol. 16(2), pages 117-119, January.
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