标题： 关于非参数回归的稳健经验似然及其在断点回归设计中的应用 显示英文标题

标题： On Robust Empirical Likelihood for Nonparametric Regression with Application to Regression Discontinuity Designs

摘要： 经验似然作为一种强大的工具，在非参数回归和回归不连续设计（RDD）中构建置信区间。原始的经验似然框架可以自然地扩展到这些设定中使用局部线性平滑器，当选择欠光滑的带宽时，Wilks 定理成立。然而，在更现实的条件下，偏倚校正版本的经验似然的一般化并不简单，并且在文献中仍然是一个未解决的挑战。本文通过提出一种新的方法，称为鲁棒经验似然，为非参数回归和RDD提供了一个令人满意的解决方案。核心思想是构造鲁棒权重，这些权重同时实现偏倚校正并考虑由估计偏倚引入的额外变异性，从而在没有额外估计步骤的情况下实现有效的置信区间构建。我们证明了在非参数回归、尖锐和模糊 RDD 设定下，在较弱的条件下 Wilks 现象仍然成立。大量的模拟研究证实了我们所提出方法的有效性，显示其在覆盖率概率和区间长度方面优于现有方法。此外，所提出的程序对带宽选择具有稳健性，使其成为实证分析中的一种灵活可靠的工具。通过两个真实数据集的应用进一步展示了其实用价值。 显示英文摘要

摘要： Empirical likelihood serves as a powerful tool for constructing confidence intervals in nonparametric regression and regression discontinuity designs (RDD). The original empirical likelihood framework can be naturally extended to these settings using local linear smoothers, with Wilks' theorem holding only when an undersmoothed bandwidth is selected. However, the generalization of bias-corrected versions of empirical likelihood under more realistic conditions is non-trivial and has remained an open challenge in the literature. This paper provides a satisfactory solution by proposing a novel approach, referred to as robust empirical likelihood, designed for nonparametric regression and RDD. The core idea is to construct robust weights which simultaneously achieve bias correction and account for the additional variability introduced by the estimated bias, thereby enabling valid confidence interval construction without extra estimation steps involved. We demonstrate that the Wilks' phenomenon still holds under weaker conditions in nonparametric regression, sharp and fuzzy RDD settings. Extensive simulation studies confirm the effectiveness of our proposed approach, showing superior performance over existing methods in terms of coverage probabilities and interval lengths. Moreover, the proposed procedure exhibits robustness to bandwidth selection, making it a flexible and reliable tool for empirical analyses. The practical usefulness is further illustrated through applications to two real datasets.