Published in tbd, 2025
This paper explores strong and weak consistency of M-estimators for non-identically distributed data.
Recommended citation: Bücher et. al. (2025+). "Consistency of M-estimators for non-identically distributed data: the case of fixed-design distributional regression"
Published in Journal of the Royal Statistical Society, Series B (Statistical Methodology), 2025
In this paper bootstrapping of block maxima estimators is considered. Consistency results and limit theorems are provivded. Large scale High Performance Cluster-powered simulation studies are conducted. The application is demonstrated via a case study involving precipation extremes at a weather station in Germany.
Recommended citation: Bücher, A., Staud, T. (2025). "Bootstrapping Estimators based on the Block Maxima Method" Journal of the Royal Statistical Society: Series B (Statistical Methodology): Vol. 87
Published in Statistics & Probability Letters, 2024
We prove a formula for the maximal correlation coefficient of the bivariate Marshall Olkin distribution that was conjectured in Lin, Lai, and Govindaraju (2016, Stat. Methodol., 29:1–9).
Recommended citation: Bücher, A., Staud, T. (2025). "On the maximal correlation coefficient for the bivariate Marshall Olkin distribution" Statistics and Probability Letters, Vol. 219, 110323.
Published in Electronic Journal of Statistics, 2024
In this paper U-statistics of multivariate disjoint and sliding block maxima for time series are considered. Limit theorems and finite-sample simulation studies are presented.
Recommended citation: Bücher, A., Staud, T. (2024). "Limit theorems for non-degenerate U-statistics of block maxima for time series" Electron. J. Statist. 18(2): 2850-2885.
Conducted at the Ruhr-University Bochum, 2024
In this thesis novel results on both the sliding and disjoint block maxima method are presented.
Supervision: Prof. Axel Bücher, Prof. Johan Segers
Conducted at the Heinrich-Heine-University Düsseldorf, 2021
In this thesis a new class of limit distributions from (M. L. Stein, 2017, Biometrika) is investigated.
Supervision: Prof. Axel Bücher, Prof. Peter Kern
Conducted at the Heinrich-Heine-University Düsseldorf, 2020
In this thesis the Domain of Attraction of the Gumbel distribution is fully characterized.
Supervision: Prof. Axel Bücher, Prof. Peter Kern