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# On approximation theorems for the Euler characteristic with applications to the bootstrap

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.

• 8 publications
• 2 publications
• 12 publications
02/16/2021

### Euler Characteristic Surfaces

We study the use of the Euler characteristic for multiparameter topologi...
05/04/2017

### Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images

We present an efficient algorithm to compute Euler characteristic curves...
06/07/2022

### Sharp L^1-Approximation of the log-Heston SDE by Euler-type methods

We study the L^1-approximation of the log-Heston SDE at equidistant time...
05/04/2020

### Bootstrapping Persistent Betti Numbers and Other Stabilizing Statistics

The present contribution investigates multivariate bootstrap procedures ...
04/27/2022

### Randomness and Statistical Inference of Shapes via the Smooth Euler Characteristic Transform

In this paper, we provide the mathematical foundations for the randomnes...
10/08/2019

### Computing oscillatory solutions of the Euler system via K-convergence

We develop a method to compute effectively the Young measures associated...
08/07/2019

### Estimation of Expected Euler Characteristic Curves of Nonstationary Smooth Gaussian Random Fields

The expected Euler characteristic (EEC) curve of excursion sets of a Gau...