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Some methods for statistical inference using high-dimensional linear models

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TitleInfo
Title
Some methods for statistical inference using high-dimensional linear models
Name (type = personal)
NamePart (type = family)
Ahmed
NamePart (type = given)
Talal
NamePart (type = date)
1990-
DisplayForm
Talal Ahmed
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Bajwa
NamePart (type = given)
Waheed U.
DisplayForm
Waheed U. Bajwa
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
chair
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
School of Graduate Studies
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (encoding = w3cdtf); (qualifier = exact)
2019
DateOther (encoding = w3cdtf); (qualifier = exact); (type = degree)
2019-10
Language
LanguageTerm (authority = ISO 639-3:2007); (type = text)
English
Abstract (type = abstract)
The ordinary linear model has been the bedrock of signal processing, statistics, and machine learning for decades. The last decade, however, has witnessed a marked transformation of this model: instead of the classical low-dimensional setting in which the sample size exceeds the number of features/predictors/variables, we are increasingly having to operate in the high-dimensional setting in which the number of variables far exceeds the sample size. Although such high-dimensional settings would ordinarily lead to ill-posed problems, the inference task has been studied under the rubric of high-dimensional statistical inference, where various notions of structure have been imposed on the model parameters to obtain unique solutions to the inference problem. While there are many statistical methods that guarantee unique solutions, these methods can easily become computationally prohibitive in ultrahigh-dimensional settings, in which the number of variables can scale exponentially with the sample size. In other cases, the traditional notions of structure on model parameters can be rather restrictive, especially when the variables naturally appear in the form of a multi-way array (tensor), as in the case of neuroimaging data analysis.
The purpose of this dissertation is to study inference using high-dimensional linear models for the cases when (i) the number of variables can scale exponentially with the number of samples, and (ii) the variables naturally form a tensor structure. Specifically, for each of these respective cases, the dissertation (i) proposes an efficient inference approach, (ii) provides high-probability performance guarantees for the proposed approach, and (iii) demonstrates efficacy of the inference approach in statistical analysis of real-world datasets.
Subject (authority = RUETD)
Topic
Electrical and Computer Engineering
Subject (authority = local)
Topic
Statistical inference
Subject (authority = LCSH)
Topic
Probabilities
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
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ETD_10247
PhysicalDescription
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application/pdf
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Extent
1 online resource (vii, 89 pages) : illustrations
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
RelatedItem (type = host)
TitleInfo
Title
School of Graduate Studies Electronic Theses and Dissertations
Identifier (type = local)
rucore10001600001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/t3-3svf-6a28
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Ahmed
GivenName
Talal
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2019-09-14 23:18:09
AssociatedEntity
Name
Talal Ahmed
Role
Copyright holder
Affiliation
Rutgers University. School of Graduate Studies
AssociatedObject
Type
License
Name
Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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Technical

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2019-09-15T22:29:47
DateCreated (point = end); (encoding = w3cdtf); (qualifier = exact)
2019-09-15T22:29:47
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