AI 中文总结
该研究针对空间干扰下基于设计的推断，指出现有框架需结果建模，模拟发现估计量偏差随结果密度衰减，还重新分析热点警务实验并给出实践建议。
AI 中文摘要
面对空间干扰时，研究人员通常希望估计空间中特定点的处理效应。Wang等人（2025）和Pollmann（2023）提出了基于设计的框架，用于估计距干预不同距离处点的溢出效应。尽管这些框架是基于设计的，但我们表明其提出的估计量依赖于无法直接观测的结果，因此需要结果建模。实际使用建模结果时，即使通常设计无偏的Horvitz-Thompson估计量也可能因建模误差产生偏差。空间结果模型的性能取决于观测结果的密度或分辨率。通过模拟，我们发现估计量的偏差随结果密度增加而衰减，但不随干预单元数量增加而衰减，且使用建模结果的标准误收敛到最优标准误。为展示空间干扰下结果建模的作用，我们重新分析了Collazos等人（2021）关于热点警务对犯罪影响的实验，并给出若干实践建议。
英文摘要
In the face of spatial interference, researchers are often interested in estimating treatment effects at specific points located in space. Wang et al. (2025) and Pollmann (2023) provide design-based frameworks for estimating spillover effects on points located across a range of distances from interventions. Although these frameworks are design-based, we show their proposed estimands rely on outcomes that are directly unobservable and therefore, require outcome modeling. When using modeled outcomes in practice, even the typically design-unbiased Horvitz-Thompson estimator can accrue bias as a result of the modeling error. The performance of spatial outcome models depends on the density or resolution of observed outcomes. Through simulation, we find that the bias of the estimators decays with increasing outcome density, but not with increasing numbers of intervention units, and standard errors using modeled outcomes converge to the oracle standard errors. To demonstrate the role of outcome modeling with spatial interference, we reanalyze an experiment from Collazos et al. (2021) on the effect of hot spots policing on crime and provide several suggestions for practice.
