  The practice of employing empirical likelihood (EL) components in place of
parametric likelihood functions in the construction of Bayesian-type procedures
has been well-addressed in the modern statistical literature. We rigorously
derive the EL prior, a Jeffreys-type prior, which asymptotically maximizes the
Shannon mutual information between data and the parameters of interest. The
focus of our approach is on an integrated Kullback-Leibler distance between the
EL-based posterior and prior density functions. The EL prior density is the
density function for which the corresponding posterior form is asymptotically
negligibly different from the EL. We show that the proposed result can be used
to develop a methodology for reducing the asymptotic bias of solutions of
general estimating equations and M-estimation schemes by removing the
first-order term. This technique is developed in a similar manner to methods
employed to reduce the asymptotic bias of maximum likelihood estimates via
penalizing the underlying parametric likelihoods by their Jeffreys invariant
priors. A real data example related to a study of myocardial infarction
illustrates the attractiveness of the proposed technique in practical aspects.
  Keywords: Asymptotic bias, Biased estimating equations, Empirical likelihood,
Expected Kullback-Leibler distance, Penalized likelihood, Reference prior.
