Conference Agenda
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Inference in Wasserstein Spaces and Optimal Transport Location: 0.004 Session Chair: Ansgar Steland | |
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Detecting change-points of univariate time series using the empirical Wasserstein distance 1: RWTH Aachen University, Germany; 2: Delft University of Technology, Netherlands In this talk we are interested in detecting change-points of univariate nonstationary time series in a nonparametric setting. We introduce statistics based on the Wasserstein distance between local empirical distribution functions of the time series which are suitable to detect change-points. The one-dimensional Wasserstein distance is characterized by the sequential quantile process, and we show that this weakly converges to a Gaussian limit. Due to the nonlinearity of the quantile process, difficulties arise from the localization. A new Bahadur representation result is needed to address this, which allows us to consider the asymptotic behavior of the empirical process instead of the quantile process. The proof of this requires further study of the modulus of continuity of the empirical process. As the limit distributions of the test statistics depend on the unknown underlying distributions, a Gaussian multiplier bootstrap scheme is introduced. Lastly, a simulation study shows how well the significance level is retained under the null hypothesis of no change, and an outlook towards the power of the tests will be given. | |
