U-quantile processes and generalized linear statistics of dependent data
| dc.contributor.author | Wendler, Martin | |
| dc.date.accessioned | 2010-10-12T09:17:51Z | |
| dc.date.available | 2010-10-12T09:17:51Z | |
| dc.date.issued | 2010-10-12 | |
| dc.description.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. | en |
| dc.identifier.uri | http://hdl.handle.net/2003/27419 | |
| dc.identifier.uri | http://dx.doi.org/10.17877/DE290R-15650 | |
| dc.language.iso | en | de |
| dc.relation.ispartofseries | Discussion Paper / SFB 823;39/2010 | |
| dc.subject | Bahadur representation | en |
| dc.subject | L-Statistics | en |
| dc.subject | mixing | en |
| dc.subject | near epoch dependence | en |
| dc.subject | U-quantile | en |
| dc.subject | U-statistics | en |
| dc.subject.ddc | 310 | |
| dc.subject.ddc | 330 | |
| dc.subject.ddc | 620 | |
| dc.title | U-quantile processes and generalized linear statistics of dependent data | en |
| dc.type | Text | de |
| dc.type.publicationtype | workingPaper | de |
| dcterms.accessRights | open access |