{
  "abstract": "Assessing treatment-effect heterogeneity is important in causal inference, particularly for functional outcomes where effects may vary over time and the common effect is unknown. We propose a nonparametric procedure that assesses treatment-effect homogeneity through a testable marginal implication. By comparing within-arm difference distributions, the construction removes the unknown common functional effect without estimating it. We measure departures between these distributions through an integrated squared discrepancy of their characteristic functionals. A full-support Gaussian integrating measure yields an explicit bounded-kernel representation and identifies equality of the difference laws without requiring moment conditions on the outcomes. We construct an unbiased generalized U-statistic that accounts for dependence among overlapping differences, derive its null, fixed-alternative, and local-alternative limits, and develop a centered multiplier bootstrap for inference. The framework extends to multiple treatment arms with a shared control. For computation, a random-direction approximation combined with a nine-state recursion reduces the cost to linear order in the sample size for fixed numerical settings. Simulation studies assess the finite-sample performance of the proposed procedure relative to several benchmark methods. An application to the Irish gas smart-metering trial illustrates its use for assessing heterogeneity in functional treatment responses.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23397",
  "author_total": 3,
  "authors": [
    {
      "name": "Yongzhen Feng"
    },
    {
      "name": "Jie Li"
    },
    {
      "name": "Xiaojun Song"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7vq5wdhv5wa8r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23397",
  "fulltext_url": null,
  "id": "7vq5wdhv5wa8r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23397",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Advanced Causal Inference Techniques"
    ]
  ],
  "openalex": "W7222924094",
  "pdf_url": "https://arxiv.org/pdf/2610.23397",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7vq5wdhv5wa8r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23397",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23397"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Testing Treatment Effect Heterogeneity with Functional Outcomes",
  "title_text": "Testing Treatment Effect Heterogeneity with Functional Outcomes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:38Z",
  "url": "https://research.draconitic.com/paper/7vq5wdhv5wa8r",
  "venue": "arXiv",
  "versions": []
}