7 citations · 18 across the 15 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…
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…
Quantifying Life Insurance Risk using Least-Squares Monte Carlo
Claus Baumgart, Johannes Krebs, Robert Lempertseder +1
This article presents a stochastic framework to quantify the biometric risk of an insurance portfolio in solvency regimes such as Solvency II or the Swiss Solvency Test (SST). The…
On limit theorems for persistent Betti numbers from dependent data
Johannes Krebs
We study persistent Betti numbers and persistence diagrams obtained from time series and random fields. It is well known that the persistent Betti function is an efficient descript…
On the asymptotic normality of persistent Betti numbers
Johannes Krebs, Wolfgang Polonik
Persistent Betti numbers are a major tool in persistent homology, a subfield of topological data analysis. Many tools in persistent homology rely on the properties of persistent Be…
The autoregression bootstrap for kernel estimates of smooth nonlinear functional time series
Johannes T. N. Krebs, Jürgen E. Franke
Functional times series have become an integral part of both functional data and time series analysis. This paper deals with the functional autoregressive model of order 1 and the…
The bootstrap in kernel regression for stationary ergodic data when both response and predictor are functions
Johannes T. N. Krebs
We consider the double functional nonparametric regression model , where the response variable is Hilbert space-valued and the covariate takes values in a pseudom…
A Note on Exponential Inequalities in Hilbert Spaces for Spatial Processes with Applications to the Functional Kernel Regression Model
Johannes T. N. Krebs
In this manuscript we present exponential inequalities for spatial lattice processes which take values in a separable Hilbert space and satisfy certain dependence conditions. We co…
A Bernstein Inequality For Spatial Lattice Processes
Eduardo Valenzuela-Domínguez, Johannes T. N. Krebs, Jürgen E. Franke
In this article we present a Bernstein inequality for sums of random variables which are defined on a spatial lattice structure. The inequality can be used to derive concentration…
A Large Deviation Inequality for -mixing Time Series and its Applications to the Functional Kernel Regression Model
Johannes T. N. Krebs
We give a new large deviation inequality for sums of random variables of the form for , fixed, where the underlying process is -mix…
A Bernstein Inequality For Exponentially Growing Graphs
Johannes T. N. Krebs
In this article we present a Bernstein inequality for sums of random variables which are defined on a graphical network whose nodes grow at an exponential rate. The inequality can…
Consistency and Asymptotic Normality of Stochastic Euler Schemes for Ordinary Differential Equations
Johannes T. N. Krebs
General stochastic Euler schemes for ordinary differential equations are studied. We give proofs on the consistency, the rate of convergence and the asymptotic normality of these p…
Orthogonal Series Estimates on Strong Spatial Mixing Data
Johannes T. N. Krebs
We study a nonparametric regression model for sample data which is defined on an -dimensional lattice structure and which is assumed to be strong spatial mixing: we use design a…
Nonparametric Density Estimation for Spatial Data with Wavelets
Johannes T. N. Krebs
Nonparametric density estimators are studied for -dimensional, strongly spatial mixing data which is defined on a general -dimensional lattice structure. We consider linear a…
Non-parametric Regression for Spatially Dependent Data with Wavelets
Johannes T. N. Krebs
We study non-parametric regression estimates for random fields. The data satisfies certain strong mixing conditions and is defined on the regular -dimensional lattice structure.…