THE EFFICIENCY OF EMPIRICAL LIKELIHOOD WITH NUISANCE PARAMETERS

In this study we check the asymptotic efficiency of empirical likelihood in the presence of nuisance parameters combined with augmented moment conditions. We show that in the presence of nuisance parameters, the asymptotic efficiency of the empirical likelihood estimator of the parameter of interest will increase by adding more moment conditions, in the sense of the positive semidefiniteness of the difference of information matrices. As a by product, we point out a necessary condition for the asymptotic efficiency to be increased when more moment condition are added.