Studentized U-quantile processes under dependence with applications to change-point analysis

Daniel Vogel*, Martin Wendler

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
6 Downloads (Pure)


Many popular robust estimators are U-quantiles, most notably the Hodges–Lehmann location estimator and the Qn scale estimator. We prove a functional central limit theorem for the U-quantile process without any moment assumptions and under weak short-range dependence conditions. We further devise an estimator for the long-run variance and show its consistency, from which the convergence of the studentized version of the U-quantile process to a standard Brownian motion follows. This result can be used to construct
CUSUM-type change-point tests based on U-quantiles, which do not rely on bootstrapping procedures. We demonstrate this approach in detail with the example of the Hodges–Lehmann estimator for robustly detecting changes in the central location. A simulation study confirms the very good efficiency and robustness properties of the test. Two real-life data sets are analyzed.
Original languageEnglish
Pages (from-to)3114-3144
Number of pages31
Issue number4B
Early online date23 May 2017
Publication statusPublished - 30 Nov 2017


  • CUSUM test
  • Hodges–Lehmann estimator
  • Long-run variance
  • Median
  • Near epoch dependence
  • Robustness
  • Weak invariance principle.


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