Wendler, Martin2010-10-122010-10-122010-10-12http://hdl.handle.net/2003/2741910.17877/DE290R-15650Generalized linear statistics are a unifying class that contains U-statistics, U-quantiles, L-statistics as well as trimmed and winsorized U-statistics. For example, many commonly used estimators of scale fall into this class. GL-statistics only have been studied under independence; in this paper, we establish the central limit theorem (CLT) and the law of the iterated logarithm (LIL) for GL-statistics of sequences which are strongly mixing or L^1 near epoch dependent on an absolutely regular process. We first investigate the empirical U-process. With the help of a generalized Bahadur representation, the CLT and the LIL for the empirical U-quantile process follow. As GL-statistics are linear functionals of the U-quantile process, the CLT and the LIL for GL-statistics are straightforward corollaries.enDiscussion Paper / SFB 823;39/2010Bahadur representationL-Statisticsmixingnear epoch dependenceU-quantileU-statistics310330620working paper