New Model-assisted Estimators for the Distribution Function Using the Pseudo Empirical Likelihood Method

This paper proposes using a model-assisted approach based on the pseudo empirical likelihood method to construct estimators for the finite population distribution function. It shows that the proposed sample-based estimators are genuine distribution functions that exhibit several attractive features, such as the fact that they do not depend on unknown parameters, and good performance at any argument is expected to be obtained. Consequently, estimation of other measures, such as quantiles, is a problem that is efficiently addressed by the proposed methodology and applications in various areas are therefore derived. Simulation studies based upon real and artificial populations show that the proposed estimators perform better than the existing ones. A practical situation in which the proposed estimators can be applied is also described.