Population empirical likelihood for nonparametric inference in survey sampling

Empirical likelihood is a popular tool for incorporating auxiliary information and constructing nonparametric confidence intervals. In survey sampling, sample elements are often selected by using an unequal probability sampling method and the empirical likelihood function needs to be modified to account for the unequal probability sampling. Wu and Rao (2006) proposed a way of constructing confidence regions using the pseudo empirical likelihood of Chen and Sitter (1999). In this paper, we propose using empirical likelihood in survey sampling based on the so-called population empirical likelihood (POEL). In the POEL approach, a single empirical likelihood is defined for the finite population. The sampling design can be incorporated into the constraint in the optimization of the POEL. For some special sampling designs, the proposed method leads to optimal estimation and does not require artificial adjustment for constructing likelihood ratio confidence intervals. Furthermore, because a single empirical likelihood is defined for the finite population, it naturally incorporates auxiliary information obtained from multiple surveys. Results from two simulation studies are presented to show the finite sample performance of the proposed method.