American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2015, 3(2), 86-88
DOI: 10.12691/ajams-3-2-8
Open AccessArticle

Robustness of Quantile Regression to Outliers

Onyedikachi O. John1,

1Department of Physical Sciences, Rhema University, Aba

Pub. Date: April 22, 2015

Cite this paper:
Onyedikachi O. John. Robustness of Quantile Regression to Outliers. American Journal of Applied Mathematics and Statistics. 2015; 3(2):86-88. doi: 10.12691/ajams-3-2-8


Sensitivity of an estimator to departures from its distributional assumptions is a very important issue that is worth considering. The influence function, which describes the effect of an infinitesimal contamination at point, y, on the estimator we are seeking, standardized by the mass, ε, of the contamination, is bounded for the median. This property of the median is enjoyed by the other quantile points. Quantile regression inherits this robustness property since the minimized objective functions in the case of sample quantile and in the case of quantile regression are the same. This robustness is investigated by analyzing the quarterly implicit price deflator using quantile regression. The coefficients for the median and other quantiles remain unchanged even when outlier is added to the data.

breakdown points infinitesimal contamination influence function quantile regression robustness outliers

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