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Convergence of U-processes in Hölder spaces with application to robust detection of a changed segment

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  • Alfredas Račkauskas

    (Vilnius University)

  • Martin Wendler

    (Otto von Guericke Universität Magdeburg)

Abstract

To detect a changed segment (so called epidemic changes) in a time series, variants of the CUSUM statistic are frequently used. However, they are sensitive to outliers in the data and do not perform well for heavy tailed data, especially when short segments get a high weight in the test statistic. We will present a robust test statistic for epidemic changes based on the Wilcoxon statistic. To study their asymptotic behavior, we prove functional limit theorems for U-processes in Hölder spaces. We also study the finite sample behavior via simulations and apply the statistic to a real data example.

Suggested Citation

  • Alfredas Račkauskas & Martin Wendler, 2020. "Convergence of U-processes in Hölder spaces with application to robust detection of a changed segment," Statistical Papers, Springer, vol. 61(4), pages 1409-1435, August.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:4:d:10.1007_s00362-020-01161-9
    DOI: 10.1007/s00362-020-01161-9
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    References listed on IDEAS

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    4. Annika Betken, 2016. "Testing for Change-Points in Long-Range Dependent Time Series by Means of a Self-Normalized Wilcoxon Test," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(6), pages 785-809, November.
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    7. Dietmar Ferger, 1994. "On the power of nonparametric changepoint-tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 41(1), pages 277-292, December.
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    Cited by:

    1. Georgy Sofronov & Martin Wendler & Volkmar Liebscher, 2020. "Editorial for the special issue: Change point detection," Statistical Papers, Springer, vol. 61(4), pages 1347-1349, August.
    2. 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.
    3. Joseph Ngatchou-Wandji & Echarif Elharfaoui & Michel Harel, 2022. "On change-points tests based on two-samples U-Statistics for weakly dependent observations," Statistical Papers, Springer, vol. 63(1), pages 287-316, February.

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