A review of recent advances in empirical likelihood

Empirical likelihood is widely used in many statistical problems. In this article, we provide a review of the empirical likelihood method, due to its significant development in recent years. Since the introduction of empirical likelihood, variants of empirical likelihood have been proposed, and the applications of empirical likelihood in high dimensions have also been studied. It is necessary to summarize the new development of empirical likelihood. In this article, we give a review of the Bayesian empirical likelihood, the bias‐corrected empirical likelihood, the jackknife empirical likelihood, the adjusted empirical likelihood, the extended empirical likelihood, the transformed empirical likelihood, the mean empirical likelihood, and the empirical likelihood with high dimensions. Finally, we have a brief survey of the computation and implementation for empirical likelihood methods.