Empirical likelihood in the presence of nuisance parameters

Empirical likelihood was introduced as a nonparametric analogue of ordinary parametric likelihood. It is well known that the empirical likelihood rati o statistic inherits a number of properties of the parametric likelihood ra tio statistic, such as the asymptotic chi-squared distribution and Bartlett correctability. This raises the question of whether or not the same is tru e in the presence of nuisance parameters. Recent work by Qin & Lawless (199 4) indicates that the chi-squared distribution is still valid to first orde r. We show that, when nuisance parameters are present, as introduced via a system of estimating equations, the asymptotic expansion for the signed squ are root of the empirical likelihood ratio statistic has a nonstandard form . This implies that the empirical likelihood ratio statistic itself does no t permit a Bartlett correction.