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The aim of this paper is to develop a change-point test for functional timeseries that uses the full functional information and is less sensitive tooutliers compared to the classical CUSUM test. For this aim, the Wilcoxontwo-sample test is generalized to functional data. To obtain the asymptoticdistribution of the test statistic, we proof a limit theorem for a process of$U$-statistics with values in a Hilbert space under weak dependence. Criticalvalues can be obtained by a newly developed version of the dependent wildbootstrap for non-degenerate 2-sample $U$-statistics.

Robust Change-Point Detection for Functional Time Series Based on $U$-Statistics and Dependent Wild Bootstrap