The least trimmed quantile regression

Authors:
N. M. Neykov;P. íek;P. Filzmoser;P. N. Neytchev
Affiliations:
National Institute of Meteorology and Hydrology, Bulgarian Academy of Sciences, 66 Tsarigradsko Chaussee, 1784 Sofia, Bulgaria;CentER, Department of Econometrics & OR, Tilburg School of Economics and Management, Tilburg University, 5000LE Tilburg, The Netherlands;Department of Statistics and Probability Theory, Vienna University of Technology, Wiedner Hauptstraíe 8-10, 1040 Vienna, Austria;National Institute of Meteorology and Hydrology, Bulgarian Academy of Sciences, 66 Tsarigradsko Chaussee, 1784 Sofia, Bulgaria
Venue:
Computational Statistics & Data Analysis
Year:
2012

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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.