The least trimmed quantile regression
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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- Čížek, Pavel, 2008.
"General Trimmed Estimation: Robust Approach To Nonlinear And Limited Dependent Variable Models,"
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- 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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- Jurecková, Jana, 2010. "Finite-sample distribution of regression quantiles," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1940-1946, December.
- Tableman, Mara, 1994. "The asymptotics of the least trimmed absolute deviations (LTAD) estimator," Statistics & Probability Letters, Elsevier, vol. 19(5), pages 387-398, April.
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