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 |
Files in This Item:
File | Description | Size | Format | |
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DP_3910_SFB823_wendler.pdf | DNB | 554.53 kB | Adobe PDF | View/Open |
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