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：本文研究回归间断设计（RDD）分析中可能出现的协变量高维问题。我们针对具有协变量选择的RDD模型提出了一套估计与推断方法，该方法在处理不同维度的协变量时均能保持稳定性能。所提方法将基于核权重的局部方法与ℓ₁-惩罚项相结合以处理高维协变量。我们通过理论分析及数值实验验证了方法的有效性：理论方面分别给出了点估计的风险性质和推断方法的覆盖性质；在特定情形下，所提估计量在额外稀疏性条件下比传统协变量调整估计量具有更高效率。数值模拟与实证案例表明，本方法在点估计的偏误和方差、推断的覆盖概率及区间长度方面均对协变量数量表现出稳健特性。