{
  "abstract": "In factorial randomized experiments with $K$ binary treatment components, we study which baseline covariates modify component main effects and interactions. We define effect-modifier cells $(j,S)$, $j\\in[p]$ and $\\emptyset\\neq S\\subseteq[K]$, through the coefficients $θ^\\ast_{jS}$ of population linear projections of conditional Walsh--Hadamard contrasts $τ_{S}$ onto standardized covariates. Using baseline-robust direct scores, we develop frequentist inference for all $p(2^K-1)$ cells. First, we prove a debiased central limit theorem with global insensitivity: the residualization baseline enters the cross-fitted score through an exactly conditionally mean-zero perturbation. The influence-function remainder therefore requires only foldwise weighted $L_2$ consistency of the baseline estimator, with no prescribed polynomial rate or nuisance product-rate condition. A separate, explicit penalty-scale condition controls the baseline's effect on the score Lasso. Second, under explicitly stated uniform nuisance, baseline, studentization, and influence-array conditions derived from bounded sparse-regression primitives, we establish a high-dimensional Gaussian approximation over the full grid, calibrated by a Walsh-spectral multiplier bootstrap. This yields simultaneous confidence bands and Romano--Wolf step-down selection of modified cells with strong familywise error control, without effect-heredity assumptions. The factorial design is fixed in the asymptotic analysis, while the covariate dimension may grow; all $2^K-1$ contrasts are covered jointly.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37382",
  "author_total": 2,
  "authors": [
    {
      "name": "Tomoshige Nakamura"
    },
    {
      "name": "Ryo Emoto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5tb3s5w0810tk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37382",
  "fulltext_url": null,
  "id": "5tb3s5w0810tk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37382",
  "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.TH"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7214971262",
  "pdf_url": "https://arxiv.org/pdf/2609.37382",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5tb3s5w0810tk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37382",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37382"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Debiased and Simultaneous Inference for Heterogeneous Factorial Effect Modifiers via Residualized Walsh-Hadamard Scores",
  "title_text": "Debiased and Simultaneous Inference for Heterogeneous Factorial Effect Modifiers via Residualized Walsh-Hadamard Scores",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:41Z",
  "url": "https://research.draconitic.com/paper/5tb3s5w0810tk",
  "venue": "arXiv",
  "versions": []
}