Find

Department of Mathematics

Functional central limit theorems for persistent Betti numbers on cylindrical networks

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Standard

Functional central limit theorems for persistent Betti numbers on cylindrical networks. / Krebs, Johannes; Hirsch, Christian.
In: Scandinavian Journal of Statistics, Vol. 49, No. 1, 03.2022, p. 427-454.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Vancouver

Krebs J, Hirsch C. Functional central limit theorems for persistent Betti numbers on cylindrical networks. Scandinavian Journal of Statistics. 2022 Mar;49(1):427-454. Epub 2021 Mar 25. doi: 10.1111/sjos.12524

Author

Krebs, Johannes ; Hirsch, Christian. / Functional central limit theorems for persistent Betti numbers on cylindrical networks. In: Scandinavian Journal of Statistics. 2022 ; Vol. 49, No. 1. pp. 427-454.

Bibtex

@article{e4be012000d84a08b647be4d9617f5ca,

title = "Functional central limit theorems for persistent Betti numbers on cylindrical networks",

abstract = "We study functional central limit theorems for persistent Betti numbers obtained from networks defined on a Poisson point process. The limit is formed in large volumes of cylindrical shape stretching only in one dimension. The results cover a directed sublevel-filtration for stabilizing networks and the Cech and Vietoris-Rips complex on the random geometric graph. The presented functional central limit theorems open the door to a variety of statistical applications in topological data analysis and we consider goodness-of-fit tests in a simulation study.",

keywords = "functional central limit theorems, goodness&#8208, of&#8208, fit tests, graphical networks, persistent Betti numbers, stochastic geometry, topological data analysis",

author = "Johannes Krebs and Christian Hirsch",

year = "2022",

month = mar,

doi = "10.1111/sjos.12524",

language = "English",

volume = "49",

pages = "427--454",

journal = "Scandinavian Journal of Statistics",

issn = "0303-6898",

publisher = "Wiley-Blackwell Publishing Ltd.",

number = "1",

}

RIS

TY - JOUR

T1 - Functional central limit theorems for persistent Betti numbers on cylindrical networks

AU - Krebs, Johannes

AU - Hirsch, Christian

PY - 2022/3

Y1 - 2022/3

N2 - We study functional central limit theorems for persistent Betti numbers obtained from networks defined on a Poisson point process. The limit is formed in large volumes of cylindrical shape stretching only in one dimension. The results cover a directed sublevel-filtration for stabilizing networks and the Cech and Vietoris-Rips complex on the random geometric graph. The presented functional central limit theorems open the door to a variety of statistical applications in topological data analysis and we consider goodness-of-fit tests in a simulation study.

AB - We study functional central limit theorems for persistent Betti numbers obtained from networks defined on a Poisson point process. The limit is formed in large volumes of cylindrical shape stretching only in one dimension. The results cover a directed sublevel-filtration for stabilizing networks and the Cech and Vietoris-Rips complex on the random geometric graph. The presented functional central limit theorems open the door to a variety of statistical applications in topological data analysis and we consider goodness-of-fit tests in a simulation study.

KW - functional central limit theorems

KW - goodness&#8208

KW - of&#8208

KW - fit tests

KW - graphical networks

KW - persistent Betti numbers

KW - stochastic geometry

KW - topological data analysis

U2 - 10.1111/sjos.12524

DO - 10.1111/sjos.12524

M3 - Journal article

VL - 49

SP - 427

EP - 454

JO - Scandinavian Journal of Statistics

JF - Scandinavian Journal of Statistics

SN - 0303-6898

IS - 1

ER -