Multiscale Scanning in Higher Dimensions: Limit theory, statistical consequences and an application in STED microscopy

König, Claudia Juliane

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

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Fakultät für Mathematik und Informatik (inkl. GAUSS) [518]

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