American Journal of Applied Mathematics and Statistics. 2015, 3(2), 86-88
DOI: 10.12691/AJAMS-3-2-8
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
Abstract
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.
Keywords
breakdown points, infinitesimal contamination, influence function, quantile regression, robustness, outliers
Copyright
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References
[1] | D. F. Andrew, P. J. Bickel, F. R. Hampel, P. J. Huber, W. H. Roger, J. W. Tukey, “Robust Estimate of Location: survey and advances,” Princeton, Princeton U. Press, 1972. |
|
[2] | P. Cizek, “Quantile Regression in XploRe Application Guide,” ed. W. Hardle, Z. Hlavka, S. Kline, Berlin, MD Tech Springer, 2003. |
|
[3] | Central Bank of Nigeria, “2012 Statistical Bulletin: Domestic Product, Consumption and Prices,” Stabull 004, 2013. |
|
[4] | B. Essama-Nssah and P. J. Lambert, “Influence Functions for Distributional Statistics,” Society for the study of Econoic Inequality, ECINEQ Working Paper Series, 2011. |
|
[5] | F. Hampel, “The Influence of Curve and its Role in Robust Estimator,” J. of the American Statistical Association, 1974, 69, p.383-393. |
|
[6] | R. Koenker, “Quantile Regression” New York, Cambgridge University Press, 2005,p.138-141 |
|
[7] | R. Koenker and G. Basset, “Regression Quantiles” Econometrica, 1978, 46, p.33-50. |
|
[8] | R. Koenker and S. Portnoy, “Quantile Regression,” University of Illinois, Urban Champaign, 1999. Available at http:/www.econ.uiuc.edu/roger/. |
|
[9] | A. N. Kolmogorov, “The method of the median in the Theory of Errors,” Mat. Sb. Reprinted in selected works of A. N. Kolmogorov, vol II, A. N. Shirayev, (ed), Kluwer: Dordrecht, 1931. |
|