EMPIRICAL LIKELIHOOD AND GENERAL ESTIMATING EQUATIONS

For some time, so-called empirical likelihoods have been used heuristi cally for purposes of nonparametric estimation. Owen showed that empir ical likelihood ratio statistics for various parameters theta(F) of an unknown distribution F have limiting chi-square distributions and may be used to obtain tests or confidence intervals in a way that is comp letely analogous to that used with parameteric likelihoods. Our object ive in this paper is twofold: first, to link estimating functions or e quations and empirical likelihood; second, to develop methods of combi ning information about parameters. We do this by assuming that informa tion about F and theta is available in the form of unbiased estimating functions. Empirical likelihoods for parameters are developed and sho wn to have properties similar to those for parameteric likelihood. Eff iciency results for estimates of both theta and F are obtained. The me thods are illustrated on several problems, and areas for future invest igation are noted.