Abstract: Inclusion of population level informations in statistical modelling is known to produce more accurate estimates than those obtained using data only from the sample. Empirical likelihood based methods can be used to combine these two kinds of information and estimate the model parameters in a computationally efficient way. Further, empirical likelihood based estimators are semiparametric and do not need any distributional assumption on the model variables. In many cases samples are drawn according to certain designs and the sampled observations have unequal probabilities of occurrence. In this article we discuss various methods to include sampling weights in empirical likelihood based estimation procedures. In particular, we consider a likelihood based estimator. This estimator dominates over the corresponding Horvitz-Thompson type estimator in many situations and can take into account the detailed structure of the sampling design. Several examples with real datasets will be considered.

This work is joint with Mark Handcock of Department of Statistics, University of Washington, Seattle, USA and Michael Rendall of Rand Corporation, USA.