Robust Change-Point Detection for Functional Time Series Based on $U$-Statistics and Dependent Wild Bootstrap
Statistics Theory
2023-06-06 v4 Methodology
Statistics Theory
Abstract
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 -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 -statistics.
Cite
@article{arxiv.2206.01458,
title = {Robust Change-Point Detection for Functional Time Series Based on $U$-Statistics and Dependent Wild Bootstrap},
author = {Lea Wegner and Martin Wendler},
journal= {arXiv preprint arXiv:2206.01458},
year = {2023}
}