<div class="csl-bib-body">
<div class="csl-entry">Fertl, L. (2021). <i>Sufficient dimension reduction using conditional variance estimation and related concepts</i> [Dissertation, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2021.92440</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2021.92440
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/18081
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dc.description.abstract
In der Regression untersucht man die bedingte Verteilung der Zielvariable gegeben den Prädiktoren, um z.B. Prognosen zu erhalten. Regression ist einer der meist studierten und angewandten Gebiet der Statistik. Die Modellierung von hochdimensionalen Daten, insbesonders bei einem nichtlinearern Zusammenhang, ist herausfordernd falls die Anzahl der Prädiktoren (p) groß ist. Suffiziente Dimensionsreduktion (SDR) ersetzt den hochdimensionalen Prädiktorvektor durch eine niedrigdimensionalere Projektion, ohne Information über die Zielvariable zu verlieren.
de
dc.description.abstract
Regression concerns modeling the conditional distribution of a target variable, the response, given a set of other variables, the predictors. Regression is the most widely used approach in Statistical applications. As such, it has been extensively studied since the field of Statistics came to existence. Modeling high-dimensional data is challenging, especially when they are nonlinearly related. Sufficient dimension reduction (SDR) considers regressions where the number of predictors (p) is large and replaces the high dimensional predictor by a lower dimensional reduction (function) without loss of information for the response.This thesis develops novel SDR approaches, the conditional variance and ensemble conditional variance estimators, for the identification and estimation of linear sufficient reductions both for the conditional mean and the conditional cumulative distribution function of the response given the multidimensional predictors. The consistency of both estimators is shown. Moreover, a combination of sufficient dimension reduction with neural networks is derived, which leverages the advantages of both in order to predict the response in the presence of abundant predictors and observations.All three proposed estimators are competitive with respect to current state-of-the-art methods in SDR methodology.
en
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
Regression
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dc.subject
Nonparametric
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dc.subject
Mean subspace
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dc.subject
Central subspace
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dc.subject
Minimum average variance estimation
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dc.subject
Sufficient Dimension reduction
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dc.title
Sufficient dimension reduction using conditional variance estimation and related concepts
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dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.identifier.doi
10.34726/hss.2021.92440
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Lukas Fertl
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dc.publisher.place
Wien
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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tuw.publication.orgunit
E105 - Institut für Stochastik und Wirtschaftsmathematik
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dc.type.qualificationlevel
Doctoral
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dc.identifier.libraryid
AC16256945
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dc.description.numberOfPages
119
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dc.thesistype
Dissertation
de
dc.thesistype
Dissertation
en
dc.rights.identifier
In Copyright
en
dc.rights.identifier
Urheberrechtsschutz
de
tuw.advisor.staffStatus
staff
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item.openaccessfulltext
Open Access
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item.openairecristype
http://purl.org/coar/resource_type/c_db06
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item.grantfulltext
open
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item.mimetype
application/pdf
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item.languageiso639-1
en
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item.openairetype
doctoral thesis
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item.fulltext
with Fulltext
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item.cerifentitytype
Publications
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crisitem.author.dept
E105-08 - Forschungsbereich Angewandte Statistik
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crisitem.author.parentorg
E105 - Institut für Stochastik und Wirtschaftsmathematik