This paper studies the case of possibly high-dimensional covariates in the regression discontinuity design (RDD) analysis. In particular, we propose estimation and inference methods for the RDD models with covariate selection which perform stably regardless of the number of covariates. The proposed methods combine the local approach using kernel weights with $\ell_{1}$-penalization to handle high-dimensional covariates. We provide theoretical and numerical results which illustrate the usefulness of the proposed methods. Theoretically, we present risk and coverage properties for our point estimation and inference methods, respectively. Under certain special case, 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 example 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.

翻译：本文研究断点回归设计（RDD）分析中可能包含高维协变量的情形。具体而言，我们提出针对含有协变量选择的RDD模型的估计与推断方法，该方法无论协变量数量多少均能保持稳定。所提出的方法结合了使用核权重的局部方法与ℓ₁罚函数来处理高维协变量。我们通过理论推导与数值实验展示了所提方法的有用性。在理论上，我们分别给出了点估计和推断方法的风险与覆盖性质。在某些特殊情形下，所提估计量在额外稀疏性条件的代价下，比传统协变量调整估计量更高效。在数值上，我们的仿真实验与实证案例表明，所提方法在点估计的偏差与方差以及推断的覆盖概率与区间长度方面，对协变量数量均展现出稳健表现。