Confidence sets for the optimal approximating model
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 1354 | |
dc.contributor.author | Rohde, Angelika | |
dc.contributor.author | Dümbgen, Lutz | |
dc.date.accessioned | 2016-03-24T17:38:25Z | |
dc.date.available | 2019-06-28T08:03:31Z | |
dc.date.issued | 2008 | |
dc.description.abstract | In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive point estimation, the construction of adaptive confidence regions is severely limited (cf. Li, 1989). The present paper sheds new light on this gap. We develop exact and adaptive confidence sets for the best approximating model in terms of risk. Our construction is based on a multiscale procedure and a particular coupling argument. Utilizing exponential inequalities for noncentral $chi^2$--distributions, we show that the risk and quadratic loss of all models within our confidence region are uniformly bounded by the minimal risk times a factor close to one. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 0946-8633 | |
dc.identifier.uri | https://doi.org/10.34657/2148 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/2052 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | eng |
dc.subject.other | Adaptivity | eng |
dc.subject.other | confidence sets | eng |
dc.subject.other | coupling | eng |
dc.subject.other | exponential inequality | eng |
dc.subject.other | model selection | eng |
dc.subject.other | multiscale inference | eng |
dc.subject.other | risk optimality | eng |
dc.title | Confidence sets for the optimal approximating model | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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