On approximation theorems for the Euler characteristic with applications to the bootstrap
We study approximation theorems for the Euler characteristic of the Vietoris-Rips and Čech filtration. The filtration is obtained from a Poisson or binomial sampling scheme in the critical regime. We apply our results to the smooth bootstrap of the Euler characteristic and determine its rate of con...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2021
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| In: |
Electronic journal of statistics
Year: 2021, Volume: 15, Issue: 2, Pages: 4462-4509 |
| ISSN: | 1935-7524 |
| DOI: | 10.1214/21-EJS1898 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1214/21-EJS1898 Verlag, lizenzpflichtig, Volltext: https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-15/issue-2/On-approximation-theorems-for-the-Euler-characteristic-with-applications-to/10.1214/21-EJS1898.full 
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| Author Notes: | Johannes Krebs, Benjamin Roycraft, Wolfgang Polonik |
| Summary: | We study approximation theorems for the Euler characteristic of the Vietoris-Rips and Čech filtration. The filtration is obtained from a Poisson or binomial sampling scheme in the critical regime. We apply our results to the smooth bootstrap of the Euler characteristic and determine its rate of convergence in the Kantorovich-Wasserstein distance and in the Kolmogorov distance. |
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| Item Description: | First available in Project Euclid: 16 September 2021 Gesehen am 29.03.2022 |
| Physical Description: | Online Resource |
| ISSN: | 1935-7524 |
| DOI: | 10.1214/21-EJS1898 |