发表机构
Georgia Institute of Technology; University of California, Santa Cruz（佐治亚理工学院; 加州大学圣克鲁兹分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对空间处理的最优设计问题，提出基于Matérn点过程的设计，通过选择最小距离$r$平衡偏差与方差，实现Horvitz-Thompson估计量的极小极大最优收敛速率，并给出渐近正态性与方差估计。
AI 中文摘要
空间处理是指分配给可能不同于响应单元所在位置的干预措施。我们在一个通用模型下研究其最优设计，在该模型中，单元的反应随其与处理地点的距离增加而减弱。我们关注的目标估计量是一种“无污染”效应，等于单个干预地点对所有假设地点的平均影响。我们提出了一种基于Matérn点过程的新颖设计，该设计将处理地点之间的距离至少分隔为$r$。较大的$r$选择通过分离干预措施减少了偏差，但通过减少其数量增加了方差。我们选择$r$以最大化Horvitz-Thompson估计量的收敛速率，并证明这是极小极大速率最优的。我们提供了估计量渐近正态性的弱条件，并提出了一种方差估计量。
英文摘要
Spatial treatments are interventions assigned to locations potentially distinct from those of the responding units. We study their optimal design under a general model in which a unit's response diminishes with distance to a treated site. Our estimand of interest is an ``uncontaminated'' effect equal to the average impact of a single intervention site over all hypothetical sites. We propose a novel design based on a Matérn point process which separates treatments by a distance of at least $r$. A larger choice of $r$ reduces bias by separating interventions but increases variance by reducing their numerosity. We choose $r$ to maximize the rate of convergence of a Horvitz-Thompson estimator and prove that this is minimax rate-optimal. We provide weak conditions under which the estimator is asymptotically normal and propose a variance estimator.
