{
  "abstract": "The parametric score test assesses a hypothesis through derivatives of the log-likelihood, whose expectation vanishes under the null. When the parameter of interest is a regression function identified as a risk minimiser, we extend this idea to test whether it belongs to a given linear function class. This yields goodness-of-fit tests for common semiparametric regression models, including generalised additive and partially linear models. Suitably formulated, the framework also detects effect modifiers in observational studies. We propose a hunt-and-test strategy that splits the data into two: on one part, after fitting the null model, machine learning is used to identify a promising direction in the empirical scores; on the other, we test whether the score vanishes in that direction. To account for error in estimating the null model, we apply a debiasing correction based on a weighted least squares projection. We establish Type I error control under relatively mild conditions and show the test has power whenever the hunted direction is correlated with the true score. Simulations and real-data examples demonstrate favourable performance, including identifying effect modifiers in an HIV clinical trial and assessing an additive model for insurance claims. The methodology is implemented in the R package dScoreTest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.28861",
  "author_total": 3,
  "authors": [
    {
      "name": "Aditya Dhawan"
    },
    {
      "name": "F. Richard Guo"
    },
    {
      "name": "Rajen D. Shah"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/egb1p7ha9cd48.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.28861",
  "fulltext_url": null,
  "id": "egb1p7ha9cd48",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.28861",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7172260159",
  "pdf_url": "https://arxiv.org/pdf/2607.28861",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/egb1p7ha9cd48.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:26Z",
      "native_id": "2607.28861",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.28861"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "The Debiased Score Test: Hunt-and-test for Semiparametric Hypotheses",
  "title_text": "The Debiased Score Test: Hunt-and-test for Semiparametric Hypotheses",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/egb1p7ha9cd48",
  "venue": "arXiv",
  "versions": []
}