Prof. Dr. Johannes Krebs

Johannes Krebs
Prof. Dr. Johannes Krebs
Holder of the Chair Mathematics - Statistics
Building KG Bau B | Room: KGB-109
Postal Address
Catholic University of Eichstätt-Ingolstadt
Faculty of Mathematics and Geography
Ostenstraße 28
85072 Eichstätt
Germany
Office hours
by appointment

Research interests

2021-2023: Advances in Topological Data Analysis funded by Deutsche Forschungsgemeinschaft (KR 4977/2-1).

2017-2020: Dynamic Objects on Random Fields funded by Deutsche Forschungsgemeinschaft (KR 4977/1-1).

 

Education

Ph.D. in Mathematics, TU Kaiserslautern, 2014-2017

M.Sc. in Mathematics, TU Kaiserslautern, 2011-2013

B.Sc. in Mathematics, TU Kaiserslautern, 2009-2011

B.Sc. in Economics, Mannheim University, 2006-2009

 

Professional experience

Full Professor, KU Eichstätt-Ingolstadt, since 2021.

Assistant Professor, Ruprecht-Karls-Universität Heidelberg, Institute of Applied Mathematics, 2021.

Postdoctoral Researcher, Ruprecht-Karls-Universität Heidelberg, Institute of Applied Mathematics, 2021.

DFG Research Fellow, Institut de statistique, biostatistique et sciences actuarielles, Université Catholique de Louvain, 2020.

Professorship substitution (at associate professor level), TU Braunschweig, Institute of Mathematical Stochastics, 2019-2020.

Professorship substitution (at associate professor level), Ruprecht-Karls-Universität Heidelberg, Institute of Applied Mathematics, 2019.

DFG Research Fellow, University of California, Davis, 2017-2019.

Postdoctoral Researcher, TU Kaiserslautern, Department of Mathematics, 2017.

Preprints & Publications

Preprints

J. Krebs and D. Rademacher (2024). Two-sample tests for relevant differences in persistence diagrams. http://arxiv.org/abs/2401.10349.

J. Krebs and D. Rademacher (2023). On the stability of the filtration functions for weakly dependent data with applications to structural break detection. arxiv.org/abs/2311.11259.

J. Krebs and W. Polonik (2019). On the asymptotic normality of persistent Betti numbers. arxiv.org/abs/1903.03280, in revision.

J. Krebs and J. Franke (2019). The autoregression bootstrap for kernel estimates of smooth nonlinear functional time series. arxiv.org/abs/1811.06172.

E. Valenzuela-Domínguez, J. Krebs and J. Franke (2019). A Bernstein inequality for spatial lattice processes. arxiv.org/abs/1702.02023.

 

Publications

D. Rademacher, J. Krebs and R. von Sachs (2024). Statistical inference for intrinsic wavelet estimators of SPD matrices in a log-Euclidean manifold. Journal of Statistical Planning and Inference, forthcoming.

J. Krebs (2024). On the Bahadur represenatation of sample quantiles for score functionals. Bernoulli, forthcoming.

C. Hirsch, J. Krebs and C. Redenbach (2023). Persistent homology based goodness-of-fit tests for spatial tessellations. Journal of Nonparametric Statistics.

B. Roycraft, J. Krebs and W. Polonik (2023). Bootstrapping persistent Betti numbers and other stabilizing statistics. The Annals of Statistics, 51 (4), 1484--1509.

J. Krebs, B. Roycraft and W. Polonik (2021) On approximation theorems for the Euler characteristic with applications to the bootstrap. Electronic Journal of Statistics, 15 (2), 4462--4509.

J. Krebs (2021) On limit theorems for persistent Betti numbers from dependent data. Stochastic processes and their Applications, 139, 139--174.

J. Krebs and C. Hirsch (2021) Functional central limit theorems for persistent Betti numbers on cylindrical networks. Scandinavian Journal of Statistics, 49 (1), 427--454.

J. Krebs (2021) A note on exponential inequalities in Hilbert spaces for spatial processes with applications to the functional kernel regression model J. Stat. Theory Pract., 15 (1), 1--24.

J. Krebs (2021) On the law of the iterated logarithm and strong invariance principles in stochastic geometry. Bernoulli, 27 (3), 1695--1723.

C. Baumgart, J. Krebs, R. Lempertseder and O. Pfaffel (2019) Quantifying life insurance risk using least-squares Monte Carlo. Der Aktuar, 2, 71--79.

J. Krebs (2019) The bootstrap in kernel regression for stationary ergodic data when both response and predictor are functions. Journal of Multivariate Analysis, 173, 620--639.

J. Krebs (2018) Non-parametric regression for spatially dependent data with wavelets. Statistics, 52, 1270--1308.

J. Krebs (2018) Nonparametric density estimation for spatial data with wavelets. Journal of Multivariate Analysis, 166, 300--319.

J. Krebs (2018) A Large Deviation Inequality for beta-mixing Time Series and its Applications to the Functional Kernel Regression Model. Statistics and Probability Letters, 133, 50--58.

J. Krebs (2018) Orthogonal series estimates on strong spatial mixing data. Journal of Statistical Planning and Inference, 193, 15--41.

J. Krebs (2017) A Bernstein inequality for exponentially growing graphs. Communications in Statistics -- Theory and Methods, 47, 5097--5106.

J. Krebs (2017) Consistency and asymptotic normality of stochastic Euler schemes for ordinary differential equations. Statistics and Probability Letters, 125, 1--8.