7 citations · 18 across the 15 of their papers we have counts for
4 papers · 1 filter
On approximation theorems for the Euler characteristic with applications to the bootstrap
Johannes Krebs, Benjamin Roycraft, Wolfgang Polonik
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…
Bootstrapping Persistent Betti Numbers and Other Stabilizing Statistics
Benjamin Roycraft, Johannes Krebs, Wolfgang Polonik
The present contribution investigates multivariate bootstrap procedures for general stabilizing statistics, with specific application to topological data analysis. Existing limit t…
Functional central limit theorems for persistent Betti numbers on cylindrical networks
Johannes Krebs, Christian Hirsch
We study functional central limit theorems for persistent Betti numbers obtained from networks defined on a Poisson point process. The limit is formed in large volumes of cylindric…
On the law of the iterated logarithm and strong invariance principles in stochastic geometry
Johannes Krebs
We study the law of the iterated logarithm (Khinchin (1924), Kolmogorov (1929)) and related strong invariance principles in stochastic geometry. As potential applications, we think…