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Functional central limit theorems for persistent Betti numbers on cylindrical networks

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...

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Hauptverfasser: Krebs, Johannes (VerfasserIn) , Hirsch, Christian (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: 2022
In: Scandinavian journal of statistics
Year: 2022, Jahrgang: 49, Heft: 1, Pages: 427-454
ISSN:1467-9469
DOI:10.1111/sjos.12524
Online-Zugang:Verlag, kostenfrei, Volltext: https://doi.org/10.1111/sjos.12524
Verlag, kostenfrei, Volltext: https://onlinelibrary.wiley.com/doi/abs/10.1111/sjos.12524
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Verfasserangaben:Johannes Krebs, Christian Hirsch

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520 |a 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 Čech 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. 
650 4 |a functional central limit theorems 
650 4 |a goodness-of-fit tests 
650 4 |a graphical networks 
650 4 |a persistent Betti numbers 
650 4 |a stochastic geometry 
650 4 |a topological data analysis 
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