On approximation theorems for the Euler characteristic with applications to the bootstrap - Krebs, Johannes; Roycraft, Benjamin; Polonik, Wolfgang (Electronic journal of statistics, 2021)
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.
First available in Project Euclid: 16 September 2021
Gesehen am 29.03.2022