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November 2017 Studentized U-quantile processes under dependence with applications to change-point analysis
Daniel Vogel, Martin Wendler
Bernoulli 23(4B): 3114-3144 (November 2017). DOI: 10.3150/16-BEJ838

Abstract

Many popular robust estimators are $U$-quantiles, most notably the Hodges–Lehmann location estimator and the $Q_{n}$ 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.

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Daniel Vogel. Martin Wendler. "Studentized U-quantile processes under dependence with applications to change-point analysis." Bernoulli 23 (4B) 3114 - 3144, November 2017. https://doi.org/10.3150/16-BEJ838

Information

Received: 1 March 2015; Revised: 1 March 2016; Published: November 2017
First available in Project Euclid: 23 May 2017

zbMATH: 06778280
MathSciNet: MR3654800
Digital Object Identifier: 10.3150/16-BEJ838

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

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Vol.23 • No. 4B • November 2017
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