{
  "abstract": "We study robust estimation of simple random tensors of arbitrary order $q\\in\\mathbb{N}$ under finite-moment assumptions and adversarial contamination. We propose the first robust estimator achieving near-optimal dimension-free statistical rates in this setting. The estimator attains the near-optimal corruption rate whenever $p\\ge2q$ moments are finite and continues to provide nontrivial guarantees throughout the weak-moment regime $q\\le p\\le2q$. Being based on directional trimmed means and minimax aggregation, our estimator is adaptive to $p$ and upper bounds on hypercontractive constants without resorting to interval-intersection procedures. Our analysis extends the trimmed-mean framework underlying recent advances in robust mean and covariance estimation to arbitrary tensor order. In particular, we establish concentration inequalities for higher-order counting and truncated empirical multi-vector product processes. We believe these inequalities could be of independent interest beyond the present application, including algorithmic robust estimation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00675",
  "author_total": 3,
  "authors": [
    {
      "name": "Roberto I. Oliveira"
    },
    {
      "name": "Zoraida F. Rico"
    },
    {
      "name": "Philip Thompson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1y6ghpy1ay7xf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00675",
  "fulltext_url": null,
  "id": "1y6ghpy1ay7xf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00675",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Advanced Statistical Methods and Models"
    ]
  ],
  "openalex": "W7206194015",
  "pdf_url": "https://arxiv.org/pdf/2609.00675",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1y6ghpy1ay7xf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.00675",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00675"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Robust dimension-free estimation of simple random tensors: optimal guarantees under heavy tails and adversarial contamination",
  "title_text": "Robust dimension-free estimation of simple random tensors: optimal guarantees under heavy tails and adversarial contamination",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:42Z",
  "url": "https://research.draconitic.com/paper/1y6ghpy1ay7xf",
  "venue": "arXiv",
  "versions": []
}