Abstract
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 language | English |
|---|---|
| Pages (from-to) | 3114-3144 |
| Number of pages | 31 |
| Journal | Bernoulli |
| Volume | 23 |
| Issue number | 4B |
| Early online date | 23 May 2017 |
| DOIs | |
| Publication status | Published - 30 Nov 2017 |
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Keywords
- CUSUM test
- Hodges–Lehmann estimator
- Long-run variance
- Median
- Near epoch dependence
- Robustness
- Weak invariance principle.
ASJC Scopus subject areas
- Statistics and Probability
Cite this
Studentized U-quantile processes under dependence with applications to change-point analysis. / Vogel, Daniel; Wendler, Martin.
In: Bernoulli, Vol. 23, No. 4B, 30.11.2017, p. 3114-3144.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Studentized U-quantile processes under dependence with applications to change-point analysis
AU - Vogel, Daniel
AU - Wendler, Martin
N1 - Acknowledgement The research was supported by the DFG Sonderforschungsbereich 823 (Collaborative Research Center) Statistik nichtlinearer dynamischer Prozesse. The authors thank Svenja Fischer and Wei Biao Wu for providing the river Elbe discharge data set and the Argentina rainfall data set, respectively. We are very grateful to the anonymous referee for the comments, which have helped to improve and clarify this manuscript.
PY - 2017/11/30
Y1 - 2017/11/30
N2 - 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 constructCUSUM-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.
AB - 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 constructCUSUM-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.
KW - CUSUM test
KW - Hodges–Lehmann estimator
KW - Long-run variance
KW - Median
KW - Near epoch dependence
KW - Robustness
KW - Weak invariance principle.
UR - http://www.scopus.com/inward/record.url?scp=85019572197&partnerID=8YFLogxK
U2 - 10.3150/16-BEJ838
DO - 10.3150/16-BEJ838
M3 - Article
VL - 23
SP - 3114
EP - 3144
JO - Bernoulli
JF - Bernoulli
SN - 1350-7265
IS - 4B
ER -