Change-Inference Based on Distance-Related Functionals: Wasserstein and Beyond

• Applicant: Professor Dr. Ansgar Steland
• Subject Area: Mathematics ; Statistics and Econometrics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 531662419

The project aims at establishing a comprehensive methodology for statistical change-point methods based on Wasserstein distances and derived functionals. The developed methods will be able to detect variations in the distribution of a data stream which go beyond classical moments, thus enabling finer analyses of characteristics such as the tail behaviour, peakedness or multi-modality. This is relevant for applications in diverse fields such as finance and environmetrics, where a change in terms of such a characteristic may indicate a structural economic break, the onset of a financial turmoil, or a tipping-point of a climate process. The analysis of such contemporary data sets is especially challenging because of the natural nonstationary of the investigated phenomena, or because of a nonstationary noise process or nuisance process. To address these issues, the project intends to develop sequential asymptotic theory for empirical Wasserstein-related functionals applicable to a suitable large class of nonstationary time series. Nonparametric test procedures will be developed to test for the presence of change-points. Further, a sequential detector will be constructed to monitor sequential data streams. The developed procedures will be studied by simulations and illustrated by analyzing real data.

• DFG Programme: Research Grants
• Co-Investigator: Dr. Fabian Mies