{
  "abstract": "We develop a robust quadratic score test for a specified mean function in functional and longitudinal data. The construction combines a convex loss with subject-level scores while retaining dependence among repeated measurements. An explicit score-centering condition ensures that the target remains the population mean. We establish the null distribution and Sobolev separation rates under sparse and dense sampling, identifying a transition from a nonparametric testing rate to the root-n boundary. A Gaussian multiplier bootstrap remains valid across these regimes, including settings with non-Gaussian quadratic limits. For implementation, we use a finite spline approximation and estimate the curvature through symmetric score increments. Under the stated conditions, the feasible procedure preserves null calibration and attains a consistency separation rate matching the lower bound over model classes containing a Gaussian submodel. Simulations illustrate the performance of squared, Huber, and absolute losses under regular errors and contamination, and an analysis of longitudinal CD4 counts demonstrates the method.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38307",
  "author_total": 2,
  "authors": [
    {
      "name": "Behdad Mostafaiy"
    },
    {
      "name": "Mustafa Abduljabbar Dawood"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7hwqw2yywf6hw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38307",
  "fulltext_url": null,
  "id": "7hwqw2yywf6hw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38307",
  "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",
      "stat.ME"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38307",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7hwqw2yywf6hw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:41Z",
      "native_id": "2610.38307",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38307"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Robust Global Testing for Mean Functions in Sparse and Dense Functional and Longitudinal Data",
  "title_text": "Robust Global Testing for Mean Functions in Sparse and Dense Functional and Longitudinal Data",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:00Z",
  "url": "https://research.draconitic.com/paper/7hwqw2yywf6hw",
  "venue": "arXiv",
  "versions": []
}