  Indirect inference estimators (i.e., simulation-based minimum distance
estimators) in a parametric model that are based on auxiliary non-parametric
maximum likelihood density estimators are shown to be asymptotically normal. If
the parametric model is correctly specified, it is furthermore shown that the
asymptotic variance-covariance matrix equals the inverse of the
Fisher-information matrix. These results are based on uniform-in-parameters
convergence rates and a uniform-in-parameters Donsker-type theorem for
non-parametric maximum likelihood density estimators.
