{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08335",
  "author_total": 2,
  "authors": [
    {
      "name": "Stefan Faridani"
    },
    {
      "name": "Michael P. Leung"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/067pnkek0q6xd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08335",
  "fulltext_url": null,
  "id": "067pnkek0q6xd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08335",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "econ.EM"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "1803|Optimal Experimental Design Methods"
    ]
  ],
  "openalex": "W7212001161",
  "pdf_url": "https://arxiv.org/pdf/2609.08335",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/067pnkek0q6xd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:07Z",
      "native_id": "2609.08335",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08335"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Designing Spatial Treatments",
  "title_text": "Designing Spatial Treatments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:07Z",
  "url": "https://research.draconitic.com/paper/067pnkek0q6xd",
  "venue": "arXiv",
  "versions": []
}