Consider a random sample from a bivariate random vector whose marginal distributions differ by a location parameter. An empirical likelihood approach with a fixed number of unknown constraints is proposed. A Wilks’ type theorem is derived, including the construction of a non-parametric confidence region and test. Then a uniform local asymptotic normality condition is established for the empirical likelihood. This is used to derive various versions of maximum empirical likelihood estimators based on the work of Peng and Schick (2018).

This is the Admission to Candidacy Exam for Mengyu Chen. The Committee members are Guifang Fu, Anton Schick (Chair), and Qiqing Yu.