Title: Studentized U-quantile processes
Authors: Carina Gerstenberger - Ruhr-Universitaet Bochum (Germany)
Daniel Vogel - University of Aberdeen (United Kingdom) [presenting]
Martin Wendler - Ernst Moritz Arndt Universitaet Greifswald (Germany)
Abstract: Functional limit theorems for U-quantiles of stationary, but potentially dependent series are studied, and a consistent estimator for the long-run variance is proposed. This allows us to formulate studentized versions of the processes, which are asymptotically distribution-free. Such results are useful, e.g., for change-point analysis. The Hodges--Lehmann estimator and the $Q_n$ estimator are popular estimators for location and scale, respectively. Both combine high efficiency at normality with appealing robustness properties, and both are U-quantiles. We propose and investigate change-point test statistics based on these estimators for detecting changes in the central location or the scale of time series. A strength of quantile-based estimators in general is ``moment-freeness''. We use the notion of near epoch dependence in probability (PNED), a very general weak dependence condition, which, in contrast to the traditional $L_2$ near epoch dependence, does not require the existence of any moments, making it particularly appealing for the analysis of robust methods under dependence.