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.
After revision: Given additional distributional information 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.