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


Many popular robust estimators are UU-quantiles, most notably the Hodges-Lehmann location estimator and the QnQ_n scale estimator. We prove a functional central limit theorem for the sequential UU-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 sequential UU-quantile process to a standard Brownian motion follows. This result can be used to construct CUSUM-type change-point tests based on UU-quantiles, which do not rely on bootstrapping procedures. We demonstrate this approach in detail at the example of the Hodges-Lehmann estimator for robustly detecting changes in the central location. A simulation study confirms the very good robustness and efficiency properties of the test. Two real-life data sets are analyzed

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