Generalised empirical likelihood-based kernel density estimation

If additional information about the distribution of a random variable is available in the form of moment conditions, a weighted kernel density estimate reflecting the extra information can be constructed by replacing the uniform weights with the generalised empirical likelihood probabilities.  It is shown that the resultant density estimator provides an improved approximation to the moment constraints.  Moreover, a reduction in variance is achieved due to the systematic use of the extra moment information.