Locally adaptive confidence bands

Simple item page
dc.contributor.authorPatschkowski, Tim
dc.contributor.authorRohde, Angelika
dc.date.accessioned2016-11-03T13:34:14Z
dc.date.available2016-11-03T13:34:14Z
dc.date.issued2016
dc.description.abstractWe develop honest and locally adaptive confidence bands for probability densities. They provide substantially improved confidence statements in case of inhomogeneous smoothness, and are easily implemented and visualized. The article contributes conceptual work on locally adaptive inference as a straightforward modification of the global setting imposes severe obstacles for statistical purposes. Among others, we introduce a statistical notion of local Hölder regularity and prove a correspondingly strong version of local adaptivity. We substantially relax the straightforward localization of the self-similarity condition in order not to rule out prototypical densities. The set of densities permanently excluded from the consideration is shown to be pathological in a mathematically rigorous sense. On a technical level, the crucial component for the verification of honesty is the identification of an asymptotically least favorable stationary case by means of Slepian's comparison inequality.en
dc.identifier.urihttp://hdl.handle.net/2003/35308
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-17351
dc.language.isoende
dc.relation.ispartofseriesDiscussion Paper / SFB823;60, 2016en
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.titleLocally adaptive confidence bandsen
dc.typeTextde
dc.type.publicationtypeworkingPaperde
dcterms.accessRightsopen access

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
DP_6016_SFB823_Patschkowski_Rohde.pdf
Size:
3.02 MB
Format:
Adobe Portable Document Format
Description:
DNB
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
3.12 KB
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

Sonderforschungsbereich (SFB) 823