Two-sample extended empirical likelihood for estimating equations

We propose a two-sample extended empirical likelihood for inference on the difference between two pp-dimensional parameters defined by estimating equations. The standard two-sample empirical likelihood for the difference is Bartlett correctable but its domain is a bounded subset of the parameter space. We expand its domain through a composite similarity transformation to derive the two-sample extended empirical likelihood which is defined on the full parameter space. The extended empirical likelihood has the same asymptotic distribution as the standard one and can also achieve the second-order accuracy of the Bartlett correction. We include two applications to illustrate the use of two-sample empirical likelihood methods and to demonstrate the superior coverage accuracy of the extended empirical likelihood confidence regions.