Designing Spatial Treatments
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 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.
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BibTeX
@misc{faridani2026designing,
title = {{Designing Spatial Treatments}},
author = {Stefan Faridani and Michael P. Leung},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08335},
eprint = {2609.08335},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08335},
}
RIS
TY - UNPB
TI - Designing Spatial Treatments
AU - Stefan Faridani
AU - Michael P. Leung
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08335
UR - https://arxiv.org/abs/2609.08335
AB - 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.
ER -