Before revision:  Same approach can be used to estimate a density or distribution of certain functions of data and, possibly, of the unknown parameters, the latter being replaced by their generalised empirical likelihood estimates. A special case of interest is estimation of densities or distributions of (generalised) residuals in semi-parametric models defined by a finite number of moment restrictions.
After revision:  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.