{
  "abstract": "The median-of-means (MoM) estimator is a robust alternative to the sample mean for heavy-tailed or contaminated data. While its non-asymptotic properties are well understood for i.i.d.\\ samples, much less is known for dependent sequences. We establish non-asymptotic deviation bounds for the MoM estimator computed from consecutive blocks of an identically distributed $α$-mixing sequence, both for a single mean and uniformly over a class of functions (the median-of-means process). All bounds remain valid, with explicitly adjusted constants, when a sufficiently small fraction of the blocks is adversarially corrupted. As applications, we obtain deviation bounds for a median-of-means Nadaraya--Watson regression estimator, for the MoM kernel density estimator, and for empirical and Bahadur-type estimators of Value-at-Risk and Conditional Value-at-Risk. Finally, we show that the sampling of bulk materials, where the measurements form a spatially dependent random field, reduces to the one-dimensional setting if the samples are taken in well-separated groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15974",
  "author_total": 2,
  "authors": [
    {
      "name": "Attila Lovas"
    },
    {
      "name": "Marcell Tukora"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/74bezwhpzyz14.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15974",
  "fulltext_url": null,
  "id": "74bezwhpzyz14",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15974",
  "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.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Advanced Statistical Methods and Models"
    ]
  ],
  "openalex": "W7221765464",
  "pdf_url": "https://arxiv.org/pdf/2610.15974",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/74bezwhpzyz14.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15974",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15974"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Robust Nonparametric Methods for $α$-Mixing Sequences via Median-of-Means",
  "title_text": "Robust Nonparametric Methods for α-Mixing Sequences via Median-of-Means",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/74bezwhpzyz14",
  "venue": "arXiv",
  "versions": []
}