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March, 1994 Empirical Likelihood and General Estimating Equations
Jin Qin, Jerry Lawless
Ann. Statist. 22(1): 300-325 (March, 1994). DOI: 10.1214/aos/1176325370


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.


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Jin Qin. Jerry Lawless. "Empirical Likelihood and General Estimating Equations." Ann. Statist. 22 (1) 300 - 325, March, 1994.


Published: March, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0799.62049
MathSciNet: MR1272085
Digital Object Identifier: 10.1214/aos/1176325370

Primary: 62E20

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.22 • No. 1 • March, 1994
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