Generalized Empirical Likelihood-Based Kernel Estimation of Spatially Similar Densities

This study concerns the estimation of spatially similar densities, each with a small number of observations. To achieve flexibility and improved efficiency, we propose kernel-based estimators that are refined by generalized empirical likelihood probability weights associated with spatial moment conditions. We construct spatial moments based on spline basis functions that facilitate desirable local customization. Monte Carlo simulations demonstrate the good performance of the proposed method. To illustruate its usefulness, we apply this method to the estimation of crop yield distributions that are known to be spatically similar.