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A0553
Title: Optimal uniform change point tests in high-dimension Authors:  Moritz Jirak - University of Vienna (Austria) [presenting]
Abstract: Consider $d$ dependent change point tests, each based on a CUSUM-statistic. We provide an asymptotic theory that allows us to deal with the maximum over all test statistics as both the sample size $n$ and $d$ tend to infinity. We achieve this either by a consistent bootstrap or an appropriate limit distribution. This allows for the construction of minimax optimal tests. In case of nested factor models these tests are even adaptive with respect to the spatial dependence structure, and the corresponding minimax rate can be expressed in terms of underlying quantiles.