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2021 On approximation theorems for the Euler characteristic with applications to the bootstrap
Johannes Krebs, Benjamin Roycraft, Wolfgang Polonik
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Electron. J. Statist. 15(2): 4462-4509 (2021). DOI: 10.1214/21-EJS1898

Abstract

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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Johannes Krebs. Benjamin Roycraft. Wolfgang Polonik. "On approximation theorems for the Euler characteristic with applications to the bootstrap." Electron. J. Statist. 15 (2) 4462 - 4509, 2021. https://doi.org/10.1214/21-EJS1898

Information

Received: 1 September 2020; Published: 2021
First available in Project Euclid: 16 September 2021

Digital Object Identifier: 10.1214/21-EJS1898

Subjects:
Primary: 60F05 , 62F40
Secondary: 60B10 , 60D05

Keywords: Binomial process , bootstrap , Čech complex , critical regime , Euler characteristics , functional central limit theorem , Normal approximation , Poisson process , Random geometric complexes , smooth bootstrap , Stochastic geometry , topological data analysis , weak convergence

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Vol.15 • No. 2 • 2021
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