Title:  A Generalized Empirical Likelihood Approach for Two-Group Comparisons Given a U-Statistic Constraint

Abstract:  A generalized empirical likelihood approach in the two-group setting with a U-statistic constraint is explained. In this case, the summands that consist of the constraints for the empirical likelihood are not independent, and a weight of each summand may not have a direct interpretation as a probability point mass, dissimilar to the common empirical likelihood constraints based on independent summands. The resulting empirical likelihood ratio statistic has asymptotically a weighted chi-square distribution (univariate cases) or a combination of weighted chi-square distributions (multivariate cases). The proposed methods applied for some well-known U-statistics have robust Type I error control under various underlying distributions including cases with the violation of exchangeability under null hypotheses. A few applications including receiver operating characteristic curve analysis and testing in a cross-over design are presented in this talk.