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.

翻译：经验似然是构建非参数回归与断点回归设计（RDD）置信区间的有力工具。原始经验似然框架可通过局部线性平滑器自然扩展至这些场景，但仅当选择欠平滑带宽时威尔克斯定理才成立。然而，在更现实的条件下推广偏差校正版本的经验似然并非易事，这一直是文献中悬而未决的难题。本文提出一种称为稳健经验似然的新方法，为非参数回归与RDD提供了令人满意的解决方案。其核心思想是构建能同时实现偏差校正并兼顾估计偏差所引入额外变异性的稳健权重，从而无需额外估计步骤即可构建有效置信区间。我们证明在非参数回归、清晰型与模糊型RDD场景中，威尔克斯现象在更弱的条件下依然成立。大量模拟研究证实了所提方法的有效性，其在覆盖概率与区间长度方面均优于现有方法。此外，该程序对带宽选择具有稳健性，成为实证分析中灵活可靠的工具。通过两个真实数据集的应用进一步展示了其实用价值。