Authors: Wendler, Martin
Title: U-quantile processes and generalized linear statistics of dependent data
Language (ISO): en
Abstract: Generalized 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.
Subject Headings: Bahadur representation
L-Statistics
mixing
near epoch dependence
U-quantile
U-statistics
URI: http://hdl.handle.net/2003/27419
http://dx.doi.org/10.17877/DE290R-15650
Issue Date: 2010-10-12
Appears in Collections:Sonderforschungsbereich (SFB) 823

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