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