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

dc.contributor.advisorWerner, Frank Dr.
dc.contributor.authorKönig, Claudia Juliane
dc.titleMultiscale Scanning in Higher Dimensions: Limit theory, statistical consequences and an application in STED microscopyde
dc.contributor.refereeWerner, Frank Dr.
dc.description.abstractengScan 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
dc.contributor.coRefereeMunk, Axel Prof. Dr.
dc.subject.engmultiscale testingde
dc.subject.engscan statisticde
dc.subject.engexponential familiesde
dc.subject.enginvariance principlede
dc.subject.engweak limitde
dc.subject.engfamily wise error ratede
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematics (PPN61756535X)de

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