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Designing Spatial Treatments

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Listed:
  • Stefan Faridani
  • Michael P. Leung

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.

Suggested Citation

  • Stefan Faridani & Michael P. Leung, 2026. "Designing Spatial Treatments," Papers 2609.08335, arXiv.org.
    • Handle: RePEc:arx:papers:2609.08335
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    References listed on IDEAS

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    1. Michael P. Leung, 2021. "Rate-Optimal Cluster-Randomized Designs for Spatial Interference," Papers 2111.04219, arXiv.org, revised Sep 2022.
    2. Michael Pollmann, 2020. "Causal Inference for Spatial Treatments," Papers 2011.00373, arXiv.org, revised Apr 2026.
    3. Michael Pollmann, 2026. "Causal Inference for Spatial Treatments," Econometrica, Econometric Society, vol. 94(5), pages 1529-1561, September.
    4. Ai, Jianhang & Kuželka, Ondřej & Wang, Yuyi, 2022. "Hoeffding and Bernstein inequalities for U-statistics without replacement," Statistics & Probability Letters, Elsevier, vol. 187(C).
    5. Stefan Faridani & Paul Niehaus, 2022. "Linear estimation of global average treatment effects," Papers 2209.14181, arXiv.org, revised Jan 2026.
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