Regularized Rao-Blackwellization

Höllwarth, Henning

An Extension of a Classical Technique  with Applications to Gibbs Point Process Statistics

dc.contributor.advisor	Schuhmacher, Dominic Prof. Dr.
dc.contributor.author	Höllwarth, Henning
dc.date.accessioned	2021-06-15T14:06:21Z
dc.date.available	2021-06-21T00:50:16Z
dc.date.issued	2021-06-15
dc.identifier.uri	http://hdl.handle.net/21.11130/00-1735-0000-0008-585D-E
dc.identifier.uri	http://dx.doi.org/10.53846/goediss-8655
dc.identifier.uri	http://dx.doi.org/10.53846/goediss-8655
dc.language.iso	eng	de
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject.ddc	510	de
dc.title	Regularized Rao-Blackwellization	de
dc.title.alternative	An Extension of a Classical Technique  with Applications to Gibbs Point Process Statistics	de
dc.type	doctoralThesis	de
dc.contributor.referee	Schuhmacher, Dominic Prof. Dr.
dc.date.examination	2020-12-03
dc.description.abstracteng	In statistics, Rao-Blackwellization is a well-known technique to improve estimators by removing ancillary information which does not help toward making inference on the parameter of interest. The present thesis reveals this concept as an inverse problem that is often ill-posed. That means, the Rao-Blackwellization generally fails to be continuous with respect to a semi-norm that measures the amount of some ancillary part of an estimator. However, if the underlying statistical model is misspecified, inference cannot go beyond that inaccuracy and hence requires a corresponding continuous surrogate for the Rao-Blackwellization. We therefore propose regularizations of the mentioned ill-posed Rao-Blackwell inverse problem and eventually, we introduce and analyze the concept of regularized Rao-Blackwellization. In classical examples, this new concept leads to new estimators and also to new interpretations of existing ones. For more complex statistical models, like several ones in Gibbs point process statistics, regularized Rao-Blackwellizations can be computed at least approximately. A simulation study where we consider the Lennard-Jones model demonstrates the computational feasibility and the benefit of these results, especially in constructing parametric bootstrap confidence regions on the basis of the maximum likelihood estimator.	de
dc.contributor.coReferee	Mattner, Lutz Prof. Dr.
dc.subject.eng	Rao-Blackwellization	de
dc.subject.eng	ill-posed inverse problems	de
dc.subject.eng	Gibbs point processes	de
dc.subject.eng	Tikhonov regularization	de
dc.subject.eng	maximum likelihood estimation	de
dc.subject.eng	confidence region	de
dc.subject.eng	misspecified statistical models	de
dc.identifier.urn	urn:nbn:de:gbv:7-21.11130/00-1735-0000-0008-585D-E-8
dc.affiliation.institute	Fakultät für Mathematik und Informatik	de
dc.subject.gokfull	Mathematics (PPN61756535X)	de
dc.description.embargoed	2021-06-21
dc.identifier.ppn	1760536229

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Fakultät für Mathematik und Informatik (inkl. GAUSS) [519]

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