Some Theoretical and Practical Aspects of Empirical Likelihood Methods for Complex Surveys

This paper provides an overview on two parallel approaches to design‐based inference with complex survey data: the pseudo empirical likelihood methods and the sample empirical likelihood methods. The general framework covers parameters defined through smooth or non‐differentiable estimating functions for analytic use of survey data as well as descriptive finite population parameters, and the theory focuses on point estimation, hypothesis tests and variable selection under an arbitrary sampling design. Major practical issues for the implementation of the methods, including computational algorithms, are briefly discussed. Results from simulation studies to compare the finite sample performances of the two approaches are presented.