{
  "abstract": "We develop closed- and open-end procedures for monitoring changes in the marginal distribution of object-valued time series. The method combines two distance-based Hilbert-space embeddings, a monitoring-time-dependent projection, and self-normalization. It is computable entirely from pairwise distances, does not require long-run variance estimation, and admits exact recursive updates. Under weak temporal dependence, the closed-end null limit is a pivotal Brownian functional. For monitoring over an unbounded horizon, we introduce a growing monitoring-time weight, establish a maximal inequality and uniform remote-tail control, and derive an open-end pivotal limit together with an equivalent fixed-interval representation for critical-value simulation. Both procedures are consistent against fixed marginal changes and retain the $n^{-1/2}$ and $n^{-1/4}$ local detection boundaries associated with the linear and quadratic projection signals. Simulations with distribution-valued time series illustrate favorable numerical properties, and an application to monthly stock-return distributions illustrates the usefulness of our procedure. Further simulations with graph-valued time series and an application to spatial point processes of seismic activity are reported in the supplementary material.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10889",
  "author_total": 3,
  "authors": [
    {
      "name": "Yi Zhang"
    },
    {
      "name": "Tim Kutta"
    },
    {
      "name": "Xiaofeng Shao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/968p8datgppxy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10889",
  "fulltext_url": null,
  "id": "968p8datgppxy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10889",
  "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",
      "1804|Advanced Statistical Process Monitoring"
    ]
  ],
  "openalex": "W7212306244",
  "pdf_url": "https://arxiv.org/pdf/2609.10889",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/968p8datgppxy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.10889",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10889"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Online Change-Point Monitoring for Object-valued Time Series",
  "title_text": "Online Change-Point Monitoring for Object-valued Time Series",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:36Z",
  "url": "https://research.draconitic.com/paper/968p8datgppxy",
  "venue": "arXiv",
  "versions": []
}