We study nonparametric distance-based (isotropic) local polynomial methods for estimating the boundary average treatment effect curve, a causal functional that captures treatment effect heterogeneity in boundary discontinuity designs. We establish identification, estimation, and inference results both pointwise and uniformly along the treatment assignment boundary. We show that the geometric regularity of the boundary, a one-dimensional manifold, plays a central role in determining feasible convergence rates and valid inference procedures. Our theoretical contributions are threefold. First, we derive uniform lower and upper bounds on the convergence rate of the misspecification bias of isotropic local polynomial estimators. Second, we obtain uniform distributional approximations that justify boundary-robust inference. Third, we establish minimax lower bounds for a broad class of nonparametric isotropic regression estimators. These results yield practical guidance for empirical implementation, including new bandwidth selection rules that adapt to local irregularities of the treatment-assignment boundary. We illustrate the proposed methods using simulation evidence and an empirical application, and provide companion general-purpose software.

翻译：我们研究了非参数距离基（各向同性）局部多项式方法，用于估计边界平均处理效应曲线——这一因果泛函在边界断点设计中捕捉处理效应的异质性。我们建立了沿处理分配边界逐点与一致性的识别、估计和推断结果。研究表明，边界的几何正则性（即一维流形）在确定可行收敛速率与有效推断流程中起核心作用。理论贡献包含三方面：第一，推导了各向同性局部多项式估计量的模型设定偏差的收敛速率统一上下界；第二，获得了支持边界稳健推断的统一分布逼近；第三，为一大类非参数各向同性回归估计量建立了极小化极大下界。这些结果为实证应用提供了实践指导，包括根据处理分配边界的局部不规则性自适应调整的带宽选择新准则。我们通过模拟实验和实证应用展示了所提方法，并提供了配套的通用软件。