  We investigate a generalized empirical likelihood approach in a two-group
setting where the constraints on parameters have a form of U-statistics. In
this situation, 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. We show that
the resulting empirical likelihood ratio statistic has a weighted chi-squared
distribution in the univariate case and a combination of weighted chi-squared
distributions in the multivariate case. Through an extensive Monte-Carlo study,
we show that the proposed methods applied for some well-known U-statistics have
robust Type I error control under various underlying distributions including
cases with a violation of exchangeability under null hypotheses. For the
application, we employ the proposed methods to test hypotheses in crossover
designs demonstrating an adaptability of the proposed methods in various
hypothesis tests.
