{
  "abstract": "Interaction trees reuse outcomes to discover treatment-effect heterogeneity, complicating inference after growth and pruning. We develop selective inference for generalized least-squares (GLS) interaction trees with a common covariate basis and known unequal variances. Under a conditional Gaussian model with positive diagonal covariance, weighted orthogonality reduces survival under additive fixed-penalty pruning to one quadratic inequality supplementing the growth event. This yields exact finite-sample conditional tests and confidence intervals, with retained-path and complete-tree inference agreeing on compatible sections. Under causal identification and a correct reference prognosis, the pruning-invariant GLS target is a signed finite-design weighted contrast of conditional average treatment effects. Simulations at $n=100,200,400,800$ and maximum depths one to three search all adjacent-observation midpoints, support calibration and demonstrate over-rejection when pruning survival is omitted. Compared with a 50:50 honest procedure, full-data learning improves reference-split recovery in some small-sample settings. Root-level median intervals can be shorter, while deep-node intervals and upper tails can be much wider; these comparisons concern each procedure's selected targets. Estimating a common scale with the variance ratio fixed produces modest changes in Selective coverage in the settings examined, without extending the exact guarantee. An exploratory ACTG 175 analysis provides a working-model illustration with estimated arm variances.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01134",
  "author_total": 1,
  "authors": [
    {
      "name": "Tomoshige Nakamura"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cr370x2dsdv71.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01134",
  "fulltext_url": null,
  "id": "cr370x2dsdv71",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01134",
  "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"
    ],
    [
      "arxiv",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01134",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cr370x2dsdv71.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:21Z",
      "native_id": "2611.01134",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01134"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Selective inference for pruned interaction trees with known unequal variances in randomized trials",
  "title_text": "Selective inference for pruned interaction trees with known unequal variances in randomized trials",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/cr370x2dsdv71",
  "venue": "arXiv",
  "versions": []
}