Problem
Research questions and friction points this paper is trying to address.
Spatial Treatments
Optimal Design
Distance Decay
Uncontaminated Effect
Horvitz-Thompson Estimator
Designing Spatial Treatments
🤖 AI Summary
研究设计了基于Matérn点过程的空间干预方案，通过调整干预点间的最小距离r来平衡偏差与方差，以估计无污染的平均干预效应。
📝 Abstract
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 Mat\'{e}rn 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Matérn point process
spatial treatments
Horvitz-Thompson estimator
minimax rate-optimal
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