{
  "abstract": "We study multiple change-point detection in multivariate time series whose distributions change in a piecewise constant manner. Distributional changes can manifest across different moment orders, from shifts in the mean and covariance to changes in higher-order moments. Higher-order moments capture increasingly rich distributional features but become difficult to estimate in high dimensions. Our tensor representation unifies moments of different orders within a common linear algebraic framework, enabling a new method to detect changes in moments of all orders up to a prescribed fixed order $p$. The resulting procedure accommodates temporal dependence and allows the dimension of the time series to grow with the sample size. Under suitable regularity conditions, the proposed procedure achieves a localization error rate that matches a newly developed minimax lower bound. We further derive limiting distributions under both nonvanishing and vanishing moment jumps and construct asymptotically valid confidence intervals in the vanishing-jump regime. Numerical experiments and real-data analyses demonstrate the method's effectiveness in detecting moment changes and a range of distributional shifts.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36594",
  "author_total": 5,
  "authors": [
    {
      "name": "Xiaokai Luo"
    },
    {
      "name": "Chenghao Xu"
    },
    {
      "name": "Haotian Xu"
    },
    {
      "name": "Carlos Misael Madrid Padilla"
    },
    {
      "name": "Daren Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f3704ewjq616j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36594",
  "fulltext_url": null,
  "id": "f3704ewjq616j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36594",
  "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.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1804|Advanced Statistical Process Monitoring"
    ]
  ],
  "openalex": "W7214933800",
  "pdf_url": "https://arxiv.org/pdf/2609.36594",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f3704ewjq616j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36594",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36594"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Optimal detection of general moment changes: Simultaneous mean and covariance change detection and beyond",
  "title_text": "Optimal detection of general moment changes: Simultaneous mean and covariance change detection and beyond",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:41Z",
  "url": "https://research.draconitic.com/paper/f3704ewjq616j",
  "venue": "arXiv",
  "versions": []
}