dc.contributor.advisor | Werner, Frank Dr. | |
dc.contributor.author | König, Claudia Juliane | |
dc.date.accessioned | 2018-07-17T08:14:42Z | |
dc.date.available | 2018-07-17T08:14:42Z | |
dc.date.issued | 2018-07-17 | |
dc.identifier.uri | http://hdl.handle.net/11858/00-1735-0000-002E-E44E-8 | |
dc.identifier.uri | http://dx.doi.org/10.53846/goediss-6968 | |
dc.language.iso | eng | de |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
dc.subject.ddc | 510 | de |
dc.title | Multiscale Scanning in Higher Dimensions: Limit theory, statistical consequences and an application in STED microscopy | de |
dc.type | doctoralThesis | de |
dc.contributor.referee | Werner, Frank Dr. | |
dc.date.examination | 2018-06-26 | |
dc.description.abstracteng | Scan statistics have a broad area of applications ranging from astrophysics over genetic screening to fluorescence microscopy. Here, we consider a calibrated scan statistic based on local likelihood ratio tests of homogeneity against heterogeneity.
The problem is to find anomalies in a d-dimensional field of independent random variables, each distributed according to a one-dimensional natural exponential family.
This thesis provides a unified methodology which controls the overall family wise error rate (FWER) to make a wrong detection at a given level. Fundamental to our method is a Gaussian approximation of the asymptotic distribution of the underlying multiscale scanning test statistic with explicit rate of convergence. From this, we obtain a weak limit theorem which can be seen as a generalized weak invariance principle to non-identically distributed data and is of independent interest. Furthermore, we give an asymptotic expansion of the procedure's power, which yields minimax optimality in case of Gaussian observations. | de |
dc.contributor.coReferee | Munk, Axel Prof. Dr. | |
dc.subject.eng | multiscale testing | de |
dc.subject.eng | scan statistic | de |
dc.subject.eng | exponential families | de |
dc.subject.eng | invariance principle | de |
dc.subject.eng | weak limit | de |
dc.subject.eng | family wise error rate | de |
dc.identifier.urn | urn:nbn:de:gbv:7-11858/00-1735-0000-002E-E44E-8-7 | |
dc.affiliation.institute | Fakultät für Mathematik und Informatik | de |
dc.subject.gokfull | Mathematics (PPN61756535X) | de |
dc.identifier.ppn | 1027040179 | |