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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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2022
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| In: |
Scandinavian journal of statistics
Year: 2022, Volume: 49, Issue: 1, Pages: 427-454 |
| ISSN: | 1467-9469 |
| DOI: | 10.1111/sjos.12524 |
| Online Access: | 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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| Author Notes: | Johannes Krebs, Christian Hirsch |
| Summary: | 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. |
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| Item Description: | First published: 12 March 2021 Gesehen am 17.04.2023 |
| Physical Description: | Online Resource |
| ISSN: | 1467-9469 |
| DOI: | 10.1111/sjos.12524 |