{
  "abstract": "Covariates missing not at random generally prevent point identification of regression coefficients without untestable restrictions. This paper studies linear regression when every missing covariate is restricted to a prespecified compact interval. The resulting population target is the set of best linear predictor coefficients compatible with the observed-data law. Under a non-atomic observed-data law and the stated regularity conditions, we can represent this identified set as the image, under the least-squares moment map, of the Aumann expectation of a random moment set. For the population set and its empirical analogue, we derive explicit bounds under bounded, sub-exponential and polynomial envelope conditions. The bounds show their dependence on sample size, dimension, confidence level and tail parameters. Under a Donsker condition and a uniform zero-set error bound, an oracle enlargement of the set-valued Z-estimator also converges at the root n rate. We separately study a Hadamard-design method for exploring the effect of admissible imputations without enumerating all vertices and build intuition to detect situations where the population target can be approximated by a zonotope. A numerical experiment illustrates how co-missingness and the width of the imputation intervals affect this diagnostic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17456",
  "author_total": 1,
  "authors": [
    {
      "name": "Hugo Dunias"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d8nw46e2qw0ag.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17456",
  "fulltext_url": null,
  "id": "d8nw46e2qw0ag",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17456",
  "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.TH"
    ],
    [
      "openalex",
      "2613|Advanced Causal Inference Techniques"
    ]
  ],
  "openalex": "W7213428115",
  "pdf_url": "https://arxiv.org/pdf/2609.17456",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d8nw46e2qw0ag.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.17456",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17456"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Finite-Sample Hausdorff Bounds and Hadamard Sensitivity for Regressions with MNAR Covariates",
  "title_text": "Finite-Sample Hausdorff Bounds and Hadamard Sensitivity for Regressions with MNAR Covariates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:51Z",
  "url": "https://research.draconitic.com/paper/d8nw46e2qw0ag",
  "venue": "arXiv",
  "versions": []
}