On approximation theorems for the Euler characteristic with applications to the bootstrap
Probability
2021-09-21 v4 Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.2005.07557,
title = {On approximation theorems for the Euler characteristic with applications to the bootstrap},
author = {Johannes Krebs and Benjamin Roycraft and Wolfgang Polonik},
journal= {arXiv preprint arXiv:2005.07557},
year = {2021}
}