Change-Point Detection Under Dependence Based on Two-Sample U-Statistics

  • Herold DehlingEmail author
  • Roland Fried
  • Isabel Garcia
  • Martin Wendler
Part of the Fields Institute Communications book series (FIC, volume 76)


We study the detection of change-points in time series. The classical CUSUM statistic for detection of jumps in the mean is known to be sensitive to outliers. We thus propose a robust test based on the Wilcoxon two-sample test statistic. The asymptotic distribution of this test can be derived from a functional central limit theorem for two-sample U-statistics. We extend a theorem of Csörgő and Horváth to the case of dependent data.


Asymptotic Distribution Block Length Functional Central Limit Theorem CUSUM Test Main Theoretical Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors wish to thank the referees for their very careful reading of an earlier version of this manuscript, and for their many thoughtful comments that helped to improve the presentation of the paper. This research was supported by the Collaborative Research Center 823, Project C3 Analysis of Structural Change in Dynamic Processes, of the German Research Foundation DFG.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Herold Dehling
    • 1
    Email author
  • Roland Fried
    • 2
  • Isabel Garcia
    • 1
  • Martin Wendler
    • 3
  1. 1.Fakultät für MathematikRuhr-Universität BochumBochumGermany
  2. 2.Fakultät für StatistikTechnische Universität DortmundDortmundGermany
  3. 3.Institut für Mathematik und InformatikErnst-Moritz-Arndt-UniversitätGreifswaldGermany

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