{
  "abstract": "Fixed-width sequential stopping rules terminate a stochastic simulation once an estimated confidence interval reaches a prescribed width. Classical fixed-width theory typically relies on a strongly consistent estimator of the asymptotic variance. This makes the normalized stopping time asymptotically deterministic, allowing fixed-sample-size limit theory to be transferred to the estimator at termination. This mechanism can fail when simulation output has infinite variance or long-range dependence. Although self-normalization and subsampling can yield asymptotically valid confidence intervals at a fixed sample size, the scaling process and the stopping time may retain nondegenerate randomness, so fixed-sample-size quantiles need not provide valid coverage at termination. In this paper, we develop a unified framework based on a joint functional limit theorem for the estimation process and a scaling process. We characterize the asymptotic behavior of both the stopping time and the self-normalized estimator evaluated at termination, thereby obtaining asymptotically valid sequential confidence intervals in classical finite-variance and infinite-variance settings. Moreover, we introduce a sequential subsampling procedure that consistently estimates the distribution relevant at the stopping time without directly estimating nuisance parameters in the limit distribution. The framework is verified for heavy-tailed moving-average processes, stochastic approximation, and an M/G/1 queue with heavy-tailed service times.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00717",
  "author_total": 3,
  "authors": [
    {
      "name": "Jose Blanchet"
    },
    {
      "name": "Peter Glynn"
    },
    {
      "name": "Wenhao Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/264qcgyx68xn2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00717",
  "fulltext_url": null,
  "id": "264qcgyx68xn2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00717",
  "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",
      "1803|Simulation Techniques and Applications"
    ]
  ],
  "openalex": "W7206156108",
  "pdf_url": "https://arxiv.org/pdf/2609.00717",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/264qcgyx68xn2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00717",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00717"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Extending Subsampling to Sequential Stopping",
  "title_text": "Extending Subsampling to Sequential Stopping",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:10Z",
  "url": "https://research.draconitic.com/paper/264qcgyx68xn2",
  "venue": "arXiv",
  "versions": []
}