A new estimator for a finite population distribution function in the presence of complete auxiliary information

In this work we propose a new estimator for the finite population distribution function of a study variable that uses knowledge about an auxiliary variable. The new estimator is based on a nonparametric superpopulation model that allows for nonlinear regression functions and not identically distributed error components. It employs two local linear regressions to estimate first the regression function and then the cdf of the error components. We propose two versions of the new estimator: a model-based version and a model-assisted one. Their performance is compared with that of several well-known estimators in a simulation study under simple random without replacement sampling and under Poisson sampling with nonconstant inclusion probabilities. The simulation results show that both versions of the new estimator perform very steadily in a great variety of populations and that they are particularly efficient in populations that are best fitted by a nonlinear regression function with regression residuals that do not follow a definite pattern.