Beschreibung:
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 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 comple...