Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 46 min ago
PreprintCC BY 4.0arXiv

Central Limit Theorems for Sample Fréchet Means of Manifold-Valued Markov Chains

  • Meshal Abuqrais
Open at sourcePDFDOICite

Abstract

In this article, we establish central limit theorems for sample Fréchet means of stationary ergodic Markov chains taking values in manifolds, extending the asymptotic theory previously developed for independent observations to a class of dependent manifold-valued processes. Our results derive the asymptotic normality of the sample Fréchet mean from a central limit condition at the population Fréchet mean, under suitable local regularity conditions. We further provide sufficient geometric and probabilistic conditions under which these assumptions hold, formulated in terms of curvature bounds and a Wasserstein mixing condition. As an application, we establish a central limit theorem for sample Fréchet means for a class of random dynamical systems generated by contractive random maps.

Related

  1. Fréchet Kriging for Metric Space-Valued Spatial Data
    Ryo Okano, Daisuke Kurisu, Hans-Georg Müller
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  2. Gaussian Fluctuations of the Gradient of the Fréchet Function and Nonstandard Asymptotics of Sample Fréchet Means
    Yutaro Nakabayashi
    arXivPreprintarXiv licenceFull textProbabilityStatisticsarXiv
  3. The hyperbolic class and vanishing laws in a TMF-valued four-manifold invariant
    Yuqi Li, Hao-Yu Sun
    arXivPreprintCC BY 4.0Full textGeometry & topologyHigh-energy & particle physicsarXiv
  4. A Note on the Cut-Locus-Corrected Fréchet Mean Central Limit Theorem
    Susovan Pal
    arXivPreprintCC BY 4.0Full textStatisticsarXiv
  5. Topological point singularities of manifold-valued maps and approximability by smooth maps
    Giacomo Canevari, Giandomenico Orlandi
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{abuqrais2026central,
  title = {{Central Limit Theorems for Sample Fréchet Means of Manifold-Valued Markov Chains}},
  author = {Meshal Abuqrais},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23258},
  eprint = {2609.23258},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23258},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Central Limit Theorems for Sample Fréchet Means of Manifold-Valued Markov Chains
AU  - Meshal Abuqrais
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23258
UR  - https://arxiv.org/abs/2609.23258
AB  - In this article, we establish central limit theorems for sample Fréchet means of stationary ergodic Markov chains taking values in manifolds, extending the asymptotic theory previously developed for independent observations to a class of dependent manifold-valued processes. Our results derive the asymptotic normality of the sample Fréchet mean from a central limit condition at the population Fréchet mean, under suitable local regularity conditions. We further provide sufficient geometric and probabilistic conditions under which these assumptions hold, formulated in terms of curvature bounds and a Wasserstein mixing condition. As an application, we establish a central limit theorem for sample Fréchet means for a class of random dynamical systems generated by contractive random maps.
ER  -