This study is motivated by the estimation of many crop yield densities, each with a small number of observations. These densities tend to resemble one another if they are spatially proximate. To gain flexibility and improve efficiency, we propose kernel-based estimators refined by empirical likelihood probability weights derived under spatially smoothed moment conditions. We construct spatially smoothed moments based on spline functions, which are robust to outliers and readily customizable. We use these methods to estimate the corn yield distributions of Iowa counties and to predict the premiums of crop insurance programs. Monte Carlo simulations and an empirical application demonstrate the good performance and usefulness of the proposed methods.

这项研究的动机是对许多作物的单产密度进行估算，而每一个都只有少量的观察结果。如果这些密度在空间上接近，则它们往往彼此相似。为了获得灵活性并提高效率，我们提出了基于核的估计量，并通过在空间平滑矩条件下得出的经验似然概率权重进行了改进。我们基于样条函数构造空间平滑的矩，该函数对异常值具有鲁棒性并且易于定制。我们使用这些方法来估算爱荷华州的玉米单产分布，并预测农作物保险计划的保费。蒙特卡洛模拟和经验应用证明了所提出方法的良好性能和实用性。