The least trimmed quantile regression

M.N. Neykov, P. Cizek, P. Filzmoser, P.N. Neytchev

Research output: Contribution to journalArticleScientificpeer-review

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.
Original languageEnglish
Pages (from-to)1757-1770
JournalComputational Statistics & Data Analysis
Volume56
Issue number6
DOIs
Publication statusPublished - 2012

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Quantile Regression
Regression Estimator
Linear regression
Estimator
Breakdown Point
Unknown Parameters
Outlier
Simulation Study
Robustness
Estimate

Cite this

Neykov, M.N. ; Cizek, P. ; Filzmoser, P. ; Neytchev, P.N. / The least trimmed quantile regression. In: Computational Statistics & Data Analysis. 2012 ; Vol. 56, No. 6. pp. 1757-1770.
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The least trimmed quantile regression. / Neykov, M.N.; Cizek, P.; Filzmoser, P.; Neytchev, P.N.

In: Computational Statistics & Data Analysis, Vol. 56, No. 6, 2012, p. 1757-1770.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Filzmoser, P.

AU - Neytchev, P.N.

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AB - 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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