Before revision: If additional information about the distribution of a random variable is available in the form of moment conditions, the weighted kernel density estimator constructed by replacing the uniform weights with the generalised empirical likelihood probabilities provides an improved approximation to the moment constraints. More importantly, a reduction in variance is achieved due to the systematic use of the extra information.
After revision: If additional information about the distribution of a random variable is available in the form of moment conditions, the weighted kernel density estimator constructed by replacing the uniform weights with the generalised empirical likelihood probabilities as weights achieve a reduction in variance is achieved due to the systematic use of the extra information.