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We propose a two-sample extended empirical likelihood for inference on thedifference between two p-dimensional parameters defined by estimatingequations. The standard two-sample empirical likelihood for the difference isBartlett correctable but its domain is a bounded subset of the parameter space.We expand its domain through a composite similarity transformation to derivethe two-sample extended empirical likelihood which is defined on the fullparameter space. The extended empirical likelihood has the same asymptoticdistribution as the standard one and can also achieve the second order accuracyof the Bartlett correction. We include two applications to illustrate the useof two-sample empirical likelihood methods and to demonstrate the superiorcoverage accuracy of the extended empirical likelihood confidence regions.

Two-sample extended empirical likelihood for estimating equations