标题： 速率最优的随机系数回归模型非参数估计 显示英文标题

标题： Rate-optimal nonparametric estimation for random coefficient regression models

摘要： 随机系数回归模型是分析未观察到的异质性的流行工具，在最近的计量经济学文献中重新引起了关注。 在本文中，我们获得了在Hölder光滑度类中估计线性随机系数模型密度的最佳逐点收敛率，并特别展示了设计密度的尾部行为如何影响该速率。 与之前的建议相反，我们提出的并达到最佳收敛率的估计量不需要除以非参数密度估计。 估计量中调参的最优选择取决于设计密度的尾部参数和Hölder类的光滑度水平，并且我们还研究了这两个参数的自适应估计。 显示英文摘要

摘要： Random coefficient regression models are a popular tool for analyzing unobserved heterogeneity, and have seen renewed interest in the recent econometric literature. In this paper we obtain the optimal pointwise convergence rate for estimating the density in the linear random coefficient model over H\"older smoothness classes, and in particular show how the tail behavior of the design density impacts this rate. In contrast to previous suggestions, the estimator that we propose and that achieves the optimal convergence rate does not require dividing by a nonparametric density estimate. The optimal choice of the tuning parameters in the estimator depends on the tail parameter of the design density and on the smoothness level of the H\"older class, and we also study adaptive estimation with respect to both parameters.