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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