A0252
Title: On robust empirical likelihood for nonparametric regression with application to regression discontinuity designs
Authors: Qin Fang - the University of Sydney (Australia) [presenting]
Shaojun Guo - Institute of Statistics and Big Data, Renmin Unversity of China (China)
Xinghao Qiao - The University of Hong Kong (Hong Kong)
Abstract: 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. A satisfactory solution is provided 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 that 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. It is demonstrated that the Wilks' phenomenon still holds under weaker conditions in nonparametric regression, sharp and fuzzy RDD settings. Moreover, the proposed procedure exhibits robustness to bandwidth selection, making it a flexible and reliable tool for empirical analyses. The practical usefulness is illustrated through extensive simulations and applications to two real datasets.
