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Robust change-point detection for functional time series based on U-statistics and dependent wild bootstrap

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  • Lea Wegner

    (Otto-von-Guericke-Universität Magdeburg)

  • Martin Wendler

    (Otto-von-Guericke-Universität Magdeburg)

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 prove 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.

Suggested Citation

  • Lea Wegner & Martin Wendler, 2024. "Robust change-point detection for functional time series based on U-statistics and dependent wild bootstrap," Statistical Papers, Springer, vol. 65(7), pages 4767-4810, September.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:7:d:10.1007_s00362-024-01577-7
    DOI: 10.1007/s00362-024-01577-7
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    References listed on IDEAS

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    Keywords

    62R10; 62G35; 62M10; 62F40;
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