{
  "abstract": "We study the estimation of bilinear forms from noisy, partially observed multilayer data. The signal follows a Tucker2 model, with shared unit and time factors across tensor layers and slice-specific cores. The missingness pattern is structured and motivated by staggered adoption designs, which are common in causal inference and related applications. We first analyze the four-block missingness pattern, the basic building block for general staggered adoption, and propose a spectral algorithm that pools information across layers and targets the functional directly. We prove a non-asymptotic mean squared error bound that exhibits a phase transition in the number of layers, showing when pooling improves estimation, and match it with a local minimax lower bound up to constants when ranks and logarithmic factors are treated as constant-order quantities. We then extend the construction to general staggered adoption designs via an anchored four-block reduction, and derive analogous theoretical guarantees. Finally, we validate our theoretical findings using synthetic and real-world data on Castle Doctrine laws and COVID-19 policies",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.06330",
  "author_total": 3,
  "authors": [
    {
      "name": "Alberto Bordino"
    },
    {
      "name": "Thomas B. Berrett"
    },
    {
      "name": "Olga Klopp"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fdx5exbn7jzq0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.06330",
  "fulltext_url": null,
  "id": "fdx5exbn7jzq0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.06330",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2605|Tensor decomposition and applications"
    ]
  ],
  "openalex": "W7167661594",
  "pdf_url": "https://arxiv.org/pdf/2607.06330",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fdx5exbn7jzq0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2607.06330",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.06330"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Estimation of Linear Functionals in Multilayer Panels under Staggered Adoption",
  "title_text": "Estimation of Linear Functionals in Multilayer Panels under Staggered Adoption",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:22Z",
  "url": "https://research.draconitic.com/paper/fdx5exbn7jzq0",
  "venue": "arXiv",
  "versions": []
}