  We derive an extended empirical likelihood for parameters defined by
estimating equations which generalizes the original empirical likelihood for
such parameters to the full parameter space. Under mild conditions, the
extended empirical likelihood has all asymptotic properties of the original
empirical likelihood. Its contours retain the data-driven shape of the latter.
It can also attain the second order accuracy. The first order extended
empirical likelihood is easy-to-use yet it is substantially more accurate than
other empirical likelihoods, including second order ones. We recommend it for
practical applications of the empirical likelihood method.
