{
  "abstract": "We extend anytime-valid inference for linear models from independent scalar outcomes to units that contribute a vector of dependent outcomes. We develop a parametric and a nonparametric treatment. For the Gaussian multivariate linear model with an unstructured error covariance, we derive a closed-form Bayes factor under the right-Haar prior and a matrix-normal mixture alternative and prove that it is an exact e-value at every sample size and a test martingale in the invariant filtration. To our knowledge, this Bayes factor is new in the generality considered here: a d x q coefficient matrix, nuisance regressors and an arbitrary fixed positive-definite prior precision under the right-Haar nuisance prior. It yields sequential Hotelling and MANOVA tests with exact confidence sequences. Under a common within-cluster design, the cluster-robust Wald statistic of a pooled regression is equal to Hotelling's T^2 statistic computed from the per-cluster least-squares summaries, giving an exact Gaussian benchmark with G-1 degrees of freedom. For general clustered population least-squares projections, the corresponding sandwich statistic is an asymptotic e-process, without Gaussian, common-design or linearity assumptions. Each treatment includes growth and first-order expected stopping-time results; under stronger regularity, direct comparisons of expected log evidence identify a fixed mixture precision that maximizes expected log growth through constant order within a specified family, for a specified frequentist alternative. Applied to randomized experiments with several outcomes, the robust procedure gives asymptotically anytime-valid joint tests, confidence ellipsoids and simultaneous confidence sequences for the vector of average treatment effects from ordinary least-squares estimates and cluster-robust standard errors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25613",
  "author_total": 1,
  "authors": [
    {
      "name": "Michael Lindon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/07yc0tp70adq2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25613",
  "fulltext_url": null,
  "id": "07yc0tp70adq2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25613",
  "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 Bayesian Inference"
    ]
  ],
  "openalex": "W7223006313",
  "pdf_url": "https://arxiv.org/pdf/2610.25613",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/07yc0tp70adq2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25613",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25613"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Anytime-Valid Inference in Linear Models with Clustered Outcomes: Exact Multivariate Tests and Cluster-Robust Confidence Sequences",
  "title_text": "Anytime-Valid Inference in Linear Models with Clustered Outcomes: Exact Multivariate Tests and Cluster-Robust Confidence Sequences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/07yc0tp70adq2",
  "venue": "arXiv",
  "versions": []
}