A0818
Title: Sliced-Wasserstein distance based change detection with sequential empirical processes
Authors: Florian Scholze - RWTH Aachen University/ University of Bamberg (Germany) [presenting]
Fabian Mies - Delft University of Technology (Netherlands)
Ansgar Steland - RWTH Aachen University (Germany)
Abstract: The purpose is to study the problem of detecting changes in the marginal distributions of a multivariate time series with a CUSUM-type detector statistic based on the (maximum-) sliced-Wasserstein distance. From a theoretical point of view, this projection-based approach has two appealing properties. Firstly, unlike the family of Wasserstein distances, it does not suffer from the curse of dimensionality, and secondly, by means of the Kantorovich duality, asymptotic properties of the detector statistic can be derived from results for function-indexed sequential empirical processes for nonstationary time series. A new (bootstrap-) functional central limit theorem is presented for sequential empirical processes and its application to the given testing problem. Practical implications, limitations, and possible extensions are discussed.
