The aim of this paper is to develop a change-point test for functional time series that uses the full functional information and is less sensitive to outliers compared to the classical CUSUM test. For this aim, the Wilcoxon two-sample test is generalized to functional data. To obtain the asymptotic distribution of the test statistic, we proof a limit theorem for a process of $U$-statistics with values in a Hilbert space under weak dependence. Critical values can be obtained by a newly developed version of the dependent wild bootstrap for non-degenerate 2-sample $U$-statistics.

翻译：本文的目的是为功能时间序列开发一个改变点测试,该测试使用全部功能信息,与古典CUSUM测试相比,对外部线不那么敏感。 为此,Wilcoxon两样样测试被普遍推广为功能数据。为了获得测试统计数据的无症状分布,我们证明在依赖性弱的Hilbert空间进行价值为美元统计过程的极限理论。新开发的非二样样本的依赖性野靴区可以获取关键值。