A new estimator for a finite population cdf in presence of auxiliary information

In this work we propose a new estimator for the finite population cdf of a study variable that combines the two approaches to exploit knowledge about an auxiliary variable used in the Chambers and Dunstan ([2]) and the Kuo ([5]) estimators. As both the latter estimators, the new estimator is based on a superpopulation model where the population values of the study variable are generated independently from a model-cdf that is allowed to depend smoothly on an auxiliary variable. Like the Chambers and Dunstan estimator, the new estimator is based on estimates for the model-cdf of the study variable that are obtained by estimating the model-mean regression function and the model-cdf of the error terms separately. In the new estimator however both estimation steps are performed by non parametric regression in order to account for superpopulation models with smooth mean regression function and error term distribution that depends smoothly on the auxiliary variable. The non parametric regression for estimating model-cdf of the error terms resembles the one used in the Kuo estimator to estimate the model-cdf of the study variable directly, without considering the model-mean regression function. We will present a simulation study which shows that the new estimator outperforms several well known estimators from literature when the error terms are independently but not identically distributed.