{
  "abstract": "We establish statistical consistency for the penalized maximum-likelihood estimator underlying CPLASS, a method for detecting changes in velocity in $d$-dimensional time-series data. The signal is modeled as a continuous piecewise-linear trajectory observed with independent Gaussian noise. Unlike classical change-in-mean models, continuity across adjacent segments couples their parameters and prevents direct application of standard segmentation arguments. Under compact parameter spaces, minimum segment-length and velocity-jump conditions, and a strengthened Schwarz information criterion penalty $ρ_k(\\log n)^γ$ with $γ>1$, we prove joint consistency of the estimated number of segments and all changepoint locations in the high-frequency regime $n\\to\\infty$. The maximum changepoint-location error is $O_{\\mathbb{P}}\\{(\\log n/n)^{1/2}\\}$. The proof first uses empirical-process theory to establish convergence of the fitted signal, variance, and likelihood for each fixed model size. It then combines overfitting and underfitting arguments with a two-stage geometric localization analysis, yielding an initial $(\\log n/n)^{1/3}$ rate that is sharpened by exploiting the local two-segment continuous piecewise-linear structure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04191",
  "author_total": 3,
  "authors": [
    {
      "name": "Linh Do"
    },
    {
      "name": "Dat Do"
    },
    {
      "name": "Scott A. McKinley"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5vrefqx8v2df3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04191",
  "fulltext_url": null,
  "id": "5vrefqx8v2df3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04191",
  "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",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7220666613",
  "pdf_url": "https://arxiv.org/pdf/2610.04191",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5vrefqx8v2df3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04191",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04191"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Consistency of penalized maximum likelihood estimation for multidimensional change-in-velocity detection",
  "title_text": "Consistency of penalized maximum likelihood estimation for multidimensional change-in-velocity detection",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:16Z",
  "url": "https://research.draconitic.com/paper/5vrefqx8v2df3",
  "venue": "arXiv",
  "versions": []
}