On approximation theorems for the Euler characteristic with applications to the bootstrap

Johannes Krebs; Benjamin Roycraft; Wolfgang Polonik

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arXiv · 2005.07557

On approximation theorems for the Euler characteristic with applications to the bootstrap

Johannes Krebs·Benjamin Roycraft·Wolfgang Polonik

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Abstract

We study approximation theorems for the Euler characteristic of the Vietoris-Rips and Cech 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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BibTeX RIS

Johannes Krebs, Benjamin Roycraft, Wolfgang Polonik. 2020-05-15. On approximation theorems for the Euler characteristic with applications to the bootstrap. https://arxiv.org/abs/2005.07557

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