  Given additional distributional information in the form of moment
restrictions, kernel density and distribution function estimators with implied
generalised empirical likelihood probabilities as weights achieve a reduction
in variance due to the systematic use of this extra information. The particular
interest here is the estimation of densities or distributions of (generalised)
residuals in semi-parametric models defined by a finite number of moment
restrictions. Such estimates are of great practical interest, being potentially
of use for diagnostic purposes, including tests of parametric assumptions on an
error distribution, goodness-of-fit tests or tests of overidentifying moment
restrictions. The paper gives conditions for the consistency and describes the
asymptotic mean squared error properties of the kernel density and distribution
estimators proposed in the paper. A simulation study evaluates the small sample
performance of these estimators. Supplements provide analytic examples to
illustrate situations where kernel weighting provides a reduction in variance
together with proofs of the results in the paper.
