{
  "abstract": "In high-dimensional two-group studies, a supplied variable set can be used directly or to learn a projection. We study how much attainable power these choices retain at fixed observation and calibration budgets. For complete unbiased random-integration statistics under Gaussian common shape, a fixed-spectrum comparison orders direction-wise power and gives an explicit criterion balancing an oracle advantage against learning loss. Joint regeneration controls level for a specified learner with unknown diagonal shape. A paired construction permits observation reuse and finite-reference calibration of fitted scores and menus. In the paired diagonal experiment, an invariant sparse likelihood-ratio benchmark provides an attainable efficiency target. Finite-amplitude bounds connect a classical bounded quadratic to this target; conditioning on the coordinate maximum yields informative complementary bounds at moderate and strong signals. Both comparisons include finite reference budgets, and null-only simulations certify local comparisons with specified fitted rules. Equal-budget experiments and a leukemia application compare aggregation, projection and fitted quadratic scores. For correlated paired data, classical sign randomization supplies a separate calibration under central symmetry. The efficiency guarantees apply to the stated experiments and signal classes; general small-budget shape efficiency and adaptation to unknown signal allocation remain open.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00865",
  "author_total": 1,
  "authors": [
    {
      "name": "Pengfei Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bxtdhc2t741c4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00865",
  "fulltext_url": null,
  "id": "bxtdhc2t741c4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00865",
  "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/2611.00865",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bxtdhc2t741c4.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:21Z",
      "native_id": "2611.00865",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00865"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Finite-Sample Calibration and Power Benchmarks in Two-Sample Random-Integration Tests",
  "title_text": "Finite-Sample Calibration and Power Benchmarks in Two-Sample Random-Integration Tests",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:15Z",
  "url": "https://research.draconitic.com/paper/bxtdhc2t741c4",
  "venue": "arXiv",
  "versions": []
}