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Title: Bootstrap in Hilbert spaces and the detection of changes in distribution Authors:  Martin Wendler - University of Greifswald (Germany) [presenting]
Abstract: The Cramer-von Mises-statistic is widely used for testing hypothesis on distribution of random variables. We propose to use it in a CUSUM type test statistic to detect changes in the marginal distribution function of time series or random fields. This can be rewritten as a change point problem with functional observations. The asymptotic distribution of the test statistics is obtained with the continuous mapping theorem from new functional central limit theorems for the partial sum process in a Hilbert space. Because the limit distribution is difficult to evaluate and depends on a high-dimensional, difficult to estimate variance parameter, we propose to use bootstrap methods. In the case of time series, we study the non-overlapping block bootstrap, in the case of random fields the dependent wild bootstrap and show the validity of these methods. In a simulation study, we will show that our test has similar performance as the classical CUSUM test in the case of a mean shift, but better power if the distribution changes in a different aspect.