  We propose a two-sample extended empirical likelihood for inference on the
difference between two p-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.
