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Contributions to the Theory of Statistical Optimal Transport

dc.contributor.advisorMunk, Axel Prof. Dr.
dc.contributor.authorStaudt, Thomas
dc.date.accessioned2022-07-01T14:44:31Z
dc.date.available2022-07-08T00:50:10Z
dc.date.issued2022-07-01
dc.identifier.urihttp://resolver.sub.uni-goettingen.de/purl?ediss-11858/14139
dc.identifier.urihttp://dx.doi.org/10.53846/goediss-9327
dc.language.isoengde
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subject.ddc510de
dc.titleContributions to the Theory of Statistical Optimal Transportde
dc.typedoctoralThesisde
dc.contributor.refereeMunk, Axel Prof. Dr.
dc.date.examination2022-06-08de
dc.description.abstractengThe 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 topic of statistical optimal transport, each of which features a distinct contribution to the field. The first article, on the lower complexity adaptation of empirical optimal transport, explores that statistical properties of the empirical optimal transport cost between different probability measures are often governed by the simpler of the two measures, not the more complex one. The second article establishes a unified approach to central limit theorems in the context of empirical optimal transport. The third article focuses on the uniqueness of dual solutions of the general optimal transport problem and derives novel criteria that greatly enhance the scope of settings where uniqueness is understood to hold. Uniqueness of the dual solutions is crucial for Gaussian limits in the corresponding central limit theorems. Finally, the fourth article studies the application of optimal transport for the purpose of measuring the dependency between random variables, establishing the concept of transport dependency.de
dc.contributor.coRefereeSchuhmacher, Dominic Prof. Dr.
dc.subject.engWasserstein distancede
dc.subject.engLower complexity adaptationde
dc.subject.engTransport dependencyde
dc.subject.engKantorovich potentialsde
dc.subject.engCurse of dimensionalityde
dc.subject.engEmpirical optimal transportde
dc.identifier.urnurn:nbn:de:gbv:7-ediss-14139-3
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematics (PPN61756535X)de
dc.description.embargoed2022-07-08de
dc.identifier.ppn1808812166
dc.identifier.orcid0000-0003-3337-0457de
dc.notes.confirmationsentConfirmation sent 2022-07-21T09:45:01de


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