{
  "abstract": "A switchback experiment alternates an entire system between treatment and control over time. It is especially useful when interactions between units can undermine standard unit-level experiments. Switchback experiments are commonly implemented on fixed temporal grids, which impose highly structured restrictions on when treatment can switch. We study a broader class of random-duration switchbacks, in which treatment and control alternate across runs whose durations are drawn from a common distribution. Under finite carryover, we show that the mean squared error of the Horvitz-Thompson estimator has a simple frequency-domain representation governed by how temporal outcome patterns align with design-induced imbalance and contamination patterns. This representation yields a tractable worst-case design criterion that can be computed directly from the duration distribution. Optimizing over even a simple two-rate family produces a run-age-dependent switching rule that reduces the asymptotic worst-case mean squared error by at least 32\\% relative to the standard independently randomized fixed-block switchback.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13698",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuchen Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eytezrbh3pg0b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13698",
  "fulltext_url": null,
  "id": "eytezrbh3pg0b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13698",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1803|Optimal Experimental Design Methods"
    ]
  ],
  "openalex": "W7213313860",
  "pdf_url": "https://arxiv.org/pdf/2609.13698",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eytezrbh3pg0b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13698",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13698"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Spectral Design of Random-Duration Switchbacks",
  "title_text": "Spectral Design of Random-Duration Switchbacks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:36Z",
  "url": "https://research.draconitic.com/paper/eytezrbh3pg0b",
  "venue": "arXiv",
  "versions": []
}