Empirical likelihood approaches in survey sampling

There are two different empirical likelihood approaches for complex sampling designs: the “pseudo-empirical likelihood ” introduced by Chen and Sitter (1999) and the “unequal probability empirical likelihood ” approach proposed by Berger and Torres (2014, 2016). Both approaches are described and reviewed critically. We do not pretend to give an exhaustive account of all the applications of empirical likelihood in survey sampling. This paper is an extended version of Berger (2018b).