It is well known that we can use the likelihood ratio statistic to test hypotheses and to construct confidence intervals in full parametric models. Recently, Owen introduced the empirical likelihood method in nonparametric models. In this paper, we generalize his results to biased sample problems. A Wilks theorem leading to a likelihood ratio confidence interval for the mean is given. Some extensions, discussion and simulations are presented.
"Empirical Likelihood in Biased Sample Problems." Ann. Statist. 21 (3) 1182 - 1196, September, 1993. https://doi.org/10.1214/aos/1176349257