A Conditional Empirical Likelihood Based Method for Model Parameter Estimation from Complex survey Datasets

Abstract: We consider an empirical likelihood framework for inference for a statistical model based on an informative sampling design. Covariate information is incorporated both through the weights and the estimating equations. The estimator is based on conditional weights. We show that under usual conditions, with population size increasing unbounded, the estimates are strongly consistent, asymptotically unbiased and normally distributed. Our framework provides additional justification for inverse probability weighted score estimators in terms of conditional empirical likelihood. In doing so, it bridges the gap between design-based and model-based modes of inference in survey sampling settings. We illustrate these ideas with an application to an electoral survey.