2 citations · 3 across the 6 of their papers we have counts for
20 papers
Persistent homology based goodness-of-fit tests for spatial tessellations
Christian Hirsch, Johannes Krebs, Claudia Redenbach
Motivated by the rapidly increasing relevance of virtual material design in the domain of materials science, it has become essential to assess whether topological properties of sto…
Statistical inference for intrinsic wavelet estimators of SPD matrices in a log-Euclidean manifold
Johannes Krebs, Daniel Rademacher, Rainer von Sachs
In this paper we treat statistical inference for an intrinsic wavelet estimator of curves of symmetric positive definite (SPD) matrices in a log-Euclidean manifold. This estimator…
On the Bahadur representation of sample quantiles for score functionals
Johannes Krebs
We establish the Bahadur representation of sample quantiles for stabilizing score functionals in stochastic geometry and study local fluctuations of the corresponding empirical dis…
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…