{
  "abstract": "When an external reference set (an anchor) is used to decompose an LLM-judge panel's error into a quality signal and a shared common-mode error, standard practice assumes the anchor is uncontaminated: its error uncorrelated with the judges' shared error. We study when that assumption can be dropped and replaced by an estimate. Under a single-common-factor model, >=2 judges and >=2 anchors point-identify the quality variance, the common-mode variance, and each anchor's contamination correlation rho_k in closed form, with an exact per-anchor-pair failure boundary; a designated clean-anchor estimator, by contrast, reports a contaminated companion anchor as fully clean once its trusted anchor is itself contaminated. Because the single-common-factor assumption is itself untestable, the estimator ships gated behind a calibrated diagnostic battery (judge-covariance dispersion; over-identification; a family-block test from judge metadata, with a family-blocked estimator that removes family-level shared-residual bias exactly), bootstrap confidence intervals with measured coverage, and a weak-identification screen. A proposition maps which violations bias rho_k, in which direction, and which evade detection. For ordinal scores we show an identification hierarchy: with all variables ordinal, rho_k is not identified at any number of anchors; with ordinal judges and >=3 continuous anchors it is, and we give an estimator for that case. On real data the validation is asymmetric, and we say so plainly: the diagnostics are validated in the rejecting direction (both real panels we test are correctly rejected by the model-adequacy pre-test), while the estimator is validated in simulation and stress-tested semi-synthetically under oracle calibration; no real panel has yet passed the pre-test, and the pre-test exists precisely to say so. All results replay offline from shipped, checksummed artifacts.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08826",
  "author_total": 1,
  "authors": [
    {
      "name": "Veerendra Kumar Sunkavalli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/45h63dct1e8nw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08826",
  "fulltext_url": null,
  "id": "45h63dct1e8nw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08826",
  "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",
      "cs.CL"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "1803|Psychometric Methodologies and Testing"
    ]
  ],
  "openalex": "W7211995273",
  "pdf_url": "https://arxiv.org/pdf/2609.08826",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/45h63dct1e8nw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:07Z",
      "native_id": "2609.08826",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08826"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "A Closed-Form Estimator and Diagnostic Battery for Anchor-Judge Error Correlation, Under a Single-Common-Factor Model",
  "title_text": "A Closed-Form Estimator and Diagnostic Battery for Anchor-Judge Error Correlation, Under a Single-Common-Factor Model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:07Z",
  "url": "https://research.draconitic.com/paper/45h63dct1e8nw",
  "venue": "arXiv",
  "versions": []
}