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

@article{Krebs2020OnAT,
  title={On approximation theorems for the Euler characteristic with applications to the bootstrap},
  author={Johannes T. N. Krebs and Benjamin Roycraft and Wolfgang Polonik},
  journal={Electronic Journal of Statistics},
  year={2020}
}
We study approximation theorems for the Euler characteristic of the Vietoris-Rips and \v 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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