Dokumente Fakultät für Mathematik und Informatik (inkl. GAUSS) nach Gutachter "Schuhmacher, Dominic Prof. Dr."
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A Central Limit Theorem for Functions on Weighted Sparse Inhomogeneous Random Graphs
(2023-07-13)We prove a central limit theorem for a certain class of functions on weighted sparse inhomogeneous random graphs. The proof uses a perturbative form of Stein's method and relies on a careful analysis of the local structure ... -
Contributions to the Theory of Statistical Optimal Transport
(2022-07-01)The application of optimal transport based methodologies for statistical purposes has experienced a surge of interest and activity in recent years. This doctoral thesis collects the work of four research articles on the ... -
Barycenters and ANOVA for Point Pattern Data
(2022-05-10)In this thesis a new metric for point patterns is developed. A heuristic algorithm is presented, that computes barycenters with respect to the new metric. The barycenters are then used in ANOVA procedures, to assess the ... -
Limit Laws for Empirical Optimal Transport
(2022-02-17)Optimal Transport (OT) has recently gained increasing attention in various fields ranging from biology to machine learning and mathematics. Especially OT based dissimilarity measures can be designed to respect the underlying ... -
The contact process in an evolving random environment
(2021-11-26)Recently, there has been an increasing interest in interacting particle systems on evolving random graphs, respectively in time evolving random environments. In this thesis a contact process in a time evolving edge random ... -
Characteristic and necessary minutiae in fingerprints
(2021-10-22)Fingerprints feature a ridge line pattern inducing an undirected orientation field (OF) which usually features some singularities. Ridges vary in width, inducing a moderately varying ridge frequency (RF). In fingerprint ... -
Regularized Rao-Blackwellization
(2021-06-15)In statistics, Rao-Blackwellization is a well-known technique to improve estimators by removing ancillary information which does not help toward making inference on the parameter of interest. The present thesis reveals ... -
Algorithms for Optimal Transport and Wasserstein Distances
(2019-02-28)Optimal Transport and Wasserstein Distance are closely related terms that do not only have a long history in the mathematical literature, but also have seen a resurgence in recent years, particularly in the context of ... -
Convergence Rates in Dynamic Network Models
(2018-02-23)The stochastic network model by Britton and Lindholm (Journal of Statistical Physics 3, 2010) describes a class of reasonably realistic dynamics for a complex system with an underlying network structure. In a closed social ... -
Convergence of the Genealogy of the Spatial Cannings Model
(2016-11-16)In this thesis we consider the genealogy of a spatial Cannings model. This is a population model in which individuals are distributed over a countable set of sites G. The reproduction of individuals at each site is ... -
Empirical Bayesian Smoothing Splines for Signals with Correlated Errors: Methods and Applications
(2016-08-12)Smoothing splines is a well stablished method in non-parametric statistics, although the selection of the smoothness degree of the regression function is rarely addressed and, instead, a two times differentiable function, ... -
Stochastic Models in Population Genetics: The Impact of Selection and Recombination
(2015-03-27)We consider gene genealogies from populations under selective pressure and take into account that genes can be reassembled during the reproduction process due to recombination. The main result is the derivation of an ... -
Statistical Inference for Propagation Processes on Complex Networks
(2014-07-29)Scientists of various research fields have discovered the advantages of network-centric analysis, which captures complex systems by networks and allows for their representation as a collection of nodes connected by links. ... -
Statistical Multiscale Segmentation: Inference, Algorithms and Applications
(2014-03-31)This thesis mainly concerns change-point models with independent observations from an exponential family with constant mean in between change-points. An inferential scheme for estimation and confidence statements based ...