Pseudo Empirical Likelihood Inference for Non-Probability Survey Samples

In this paper, the authors first provide an overview of two major developments on complex survey data analysis: the empirical likelihood methods and statistical inference with non-probability survey samples, and highlight the important research contributions to the field of survey sampling in general and the two topics in particular by Canadian survey statisticians. The authors then propose new inferential procedures on analyzing non-probability survey samples through the pseudo empirical likelihood approach. The proposed methods lead to asymptotically equivalent point estimators that have been discussed in the recent literature but possess more desirable features on confidence intervals such as range-respecting and data-driven orientation. Results from a simulation study demonstrate the superiority of the proposed methods in dealing with binary response variables.