In this paper, a quantile model-assisted approach is used in order to estimate a finite population total. This type of estimator attempts to make efficient use of auxiliary information under the presence of influential points. The approach consists in minimizing a weighted sum of the distances between fitted and observed values. Firstly, an estimator for the quantile regression coefficients for finite populations is obtained and then, a GREG form estimator for the finite population total is presented. The performance of the proposed estimator is assessed empirically via simulation studies under different single auxiliary variable scenarios on the distribution of the errors and the existence of different types of unusual data such as outliers and influential points. The proposed estimator for the finite population total has smaller bias and mean square error under simulated scenarios of mixed normal distributions, strong heteroscedasticity in the errors and under the presence of influential points.

References:

Cässel,C., Särndal, C & Wretman, J. (1976), Some results on generalized difference estimation and generalized regression estimation for finite population, Biometrika 80, 107-116.

Wang J. & Opsomer J.D. (2010), On the asympotic normality and variance estimation for nondifferentiable survey estimations,To appear in Biometrika.

Gutierrez H. A. & F. Breid (2009), Estimaciόn del total poblacional usando el estimador de diferencia generalizada y los rangos de Wilcoxon, Revista Colombiana de estadística, 32, 123-143.

Koenker, R (2005), Quantile Regression. Cambridge University Press, UK.

Särndal, C., Swensson, B & Wretman, J (1992), Model Assisted Survey Sampling, Springer-Verlag, New York, USA.

Keywords: Quantile regression; Genaralized regression estimation; Model-assisted survey sampling

Biography: José Fernando Zea got a MsC degree from the National University of Colombia at Bogota. He has also got a BsC. in Statistics from the same University and his principal resarch areas are Survey Sampling, Statistical Computing and Bayesian Statistics. He has been a lecturer at National University of Colombia and Santo Tomas University. He has also worked at DANE (Office for National Statistics in Colombia).