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AuthorWagner, Christiandc.contributor.author
Date of accession2016-03-14T15:20:08Zdc.date.accessioned
Available in OPARU since2016-03-14T15:20:08Zdc.date.available
Year of creation2009dc.date.created
AbstractThe main focus of this work lies on generalizations of the usual nonparametric density estimation problem to cases where one does not have access to the data associated with the density of interest directly. In the first part errors-in-variables models are studied, where the data is disturbed by additive error effects. The purpose here is to get results, when the strong assumption that one knows the distribution of the errors is not suitable. Therefore, on the one hand rates of consistency for two approximative deconvolution procedures are proved - the so-called TAYLEX and SIMEX methods, on the other hand new models are introduced, where only contaminated data, but with different contamination, is used to derive consistent estimators. In these new models, in some situations a deterioration of the convergence rates appears, compared to the rates for a completely known error distribution. Yet, it is to be expected that the rates from classical models are not attainable here. In a second part it is assumed that some of the observations are measurements where the quantity of interest is accumulated. This situation is described by the aggregated data models. There new estimators for density estimation are introduced that are able to use data with different group sizes. It is shown here that these estimators reach the optimal rates of convergence attainable in the studied setting. Both in errors-in-variables models and in aggregated data models it was possible to introduce estimation procedures that fit realistic datasets better than the classical approaches.dc.description.abstract
Languageendc.language.iso
PublisherUniversität Ulmdc.publisher
LicenseStandard (Fassung vom 01.10.2008)dc.rights
Link to license texthttps://oparu.uni-ulm.de/xmlui/license_v2dc.rights.uri
KeywordAggregated data modelsdc.subject
KeywordDeconvolutiondc.subject
KeywordDensity estimationdc.subject
KeywordErrors-in-variablesdc.subject
KeywordMISEdc.subject
KeywordOptimality of ratesdc.subject
KeywordRates of consistencydc.subject
KeywordSIMEXdc.subject
KeywordTAYLEXdc.subject
Dewey Decimal GroupDDC 510 / Mathematicsdc.subject.ddc
LCSHEstimation theorydc.subject.lcsh
TitleDeconvolution problems in density estimationdc.title
Resource typeDissertationdc.type
DOIhttp://dx.doi.org/10.18725/OPARU-1089dc.identifier.doi
PPN602674417dc.identifier.ppn
URNhttp://nbn-resolving.de/urn:nbn:de:bsz:289-vts-68582dc.identifier.urn
GNDEntfaltung <Mathematik>dc.subject.gnd
FacultyFakultät für Mathematik und Wirtschaftswissenschaftenuulm.affiliationGeneral
Date of activation2009-06-18T14:49:24Zuulm.freischaltungVTS
Peer reviewneinuulm.peerReview
Shelfmark print versionZ: J-H 13.296; N: J-H 9.860uulm.shelfmark
DCMI TypeTextuulm.typeDCMI
VTS ID6858uulm.vtsID
CategoryPublikationenuulm.category
Bibliographyuulmuulm.bibliographie


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