{
  "abstract": "Goodness-of-fit testing is a basic tool for assessing whether a fitted procedure has captured the systematic information contained in the covariates. While traditional theory has largely focused on parametric regression models, modern data analysis increasingly relies on flexible black-box learners, whose predictive success alone is insufficient to assess model accuracy. In this paper, we propose SPARK, a general framework for goodness-of-fit testing that applies to traditional statistical models and general black-box learning procedures, continuous and binary responses, and low- and high-dimensional predictors. Based on a debiasing strategy, the residuals from an initial fit of a learning procedure are projected onto nearly orthogonal directions to extract any remaining signal. To capture information across all projection directions, we propose a kernel-based projection method and establish both its asymptotic properties and the consistency of a bootstrap procedure. Comprehensive simulations and real data analyses illustrate the effectiveness and flexibility of our proposed method.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37705",
  "author_total": 3,
  "authors": [
    {
      "name": "Xingwei Liu"
    },
    {
      "name": "Yuhong Yang"
    },
    {
      "name": "Wangli Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1s95ycjdtpwgj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37705",
  "fulltext_url": null,
  "id": "1s95ycjdtpwgj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37705",
  "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.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7214885110",
  "pdf_url": "https://arxiv.org/pdf/2609.37705",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1s95ycjdtpwgj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37705",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37705"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "SPARK: A General Goodness-of-Fit Assessment via Residual Projection",
  "title_text": "SPARK: A General Goodness-of-Fit Assessment via Residual Projection",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:41Z",
  "url": "https://research.draconitic.com/paper/1s95ycjdtpwgj",
  "venue": "arXiv",
  "versions": []
}