REGRESSION DISCONTINUITY DESIGN WITH POTENTIALLY MANY COVARIATES
研究了断点回归分析中高维协变量的处理，提出了结合核权重和L1惩罚的估计与推断方法，在理论上证明了其风险与覆盖性质，并通过模拟和实证展示了其稳健性。
This article examines high-dimensional covariates in regression discontinuity design (RDD) analysis. We introduce estimation and inference methods for the RDD models that incorporate covariate selection while maintaining stability across various numbers of covariates. The proposed methods combine a localization approach using kernel weights with $\ell _{1}$ -penalization to handle high-dimensional covariates. We provide both theoretical and numerical evidence demonstrating the efficacy of our methods. Theoretically, we present risk and coverage properties for our point estimation and inference methods. Conditions are given under which the proposed estimator becomes more efficient than the conventional covariate adjusted estimator at the cost of an additional sparsity condition. Numerically, our simulation experiments and empirical examples show the robust behaviors of the proposed methods to the number of covariates in terms of bias and variance for point estimation and coverage probability and interval length for inference.