The Annals of Statistics

Empirical Likelihood and General Estimating Equations

Jin Qin and Jerry Lawless

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For some time, so-called empirical likelihoods have been used heuristically for purposes of nonparametric estimation. Owen showed that empirical 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 completely analogous to that used with parametric likelihoods. Our objective in this paper is twofold: first, to link estimating functions or equations and empirical likelihood; second, to develop methods of combining information about parameters. We do this by assuming that information about $F$ and $\theta$ is available in the form of unbiased estimating functions. Empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood. Efficiency results for estimates of both $\theta$ and $F$ are obtained. The methods are illustrated on several problems, and areas for future investigation are noted.

Article information

Ann. Statist., Volume 22, Number 1 (1994), 300-325.

First available in Project Euclid: 11 April 2007

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Primary: 62E20: Asymptotic distribution theory

Asymptotic efficiency auxiliary information empirical likelihood estimating equations parametric likelihood semiparametric models testing hypotheses Wilks' theorem


Qin, Jin; Lawless, Jerry. Empirical Likelihood and General Estimating Equations. Ann. Statist. 22 (1994), no. 1, 300--325. doi:10.1214/aos/1176325370.

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