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Topics in high-dimensional inference

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TypeOfResource
Text
TitleInfo (ID = T-1)
Title
Topics in high-dimensional inference
SubTitle
PartName
PartNumber
NonSort
Identifier (displayLabel = ); (invalid = )
ETD_1970
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000051836
Language (objectPart = )
LanguageTerm (authority = ISO639-2); (type = code)
eng
Genre (authority = marcgt)
theses
Subject (ID = SBJ-1); (authority = RUETD)
Topic
Statistics and Biostatistics
Subject (ID = SBJ-2); (authority = ETD-LCSH)
Topic
Mathematical statistics
Abstract
This thesis concerns three connected problems in high-dimensional inference: compound estimation of normal means, nonparametric regression and penalization method for variable selection.
In the first part of the thesis, we propose a general maximum likelihood empirical Bayes (GMLEB) method for the compound estimation of normal means. We prove that under mild moment conditions on the unknown means, the GMLEB enjoys the adaptive ration optimality and adaptive minimaxity. Simulation experiments demonstrate that the GMLEB outperforms the James-Stein and several state-of-the-art threshold estimators in a wide range of settings.
In the second part, we explore the GMLEB wavelet method for nonparametric regression. We show that the estimator is adaptive minimax in all Besov balls. Simulation experiments on the standard test functions demonstrate that the GMLEB outperforms several threshold estimators with moderate and large samples. Applications to high-throughput screening (HTS) data are used to show the excellent performance of the approach.
In the third part, we develop a generalized penalized linear unbiased selection (GPLUS) algorithm to compute the solution paths of concave-penalized negative log-likelihood for generalized linear model. We implement the smoothly clipped absolute deviation (SCAD) and minimax concave (MC) penalties in our simulation study to demonstrate the feasibility of the proposed algorithm and their superior selection accuracy compared with the ell_1 penalty.
PhysicalDescription
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electronic resource
Extent
xii, 123 p. : ill.
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application/pdf
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text/xml
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references (p. 117-122)
Note (type = statement of responsibility)
by Wenhua Jiang
Name (ID = NAME-1); (type = personal)
NamePart (type = family)
Jiang
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Wenhua
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1981-
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author
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Wenhua Jiang
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Zhang
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Cun-Hui
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chair
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Advisory Committee
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Cun-Hui Zhang
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Strawderman
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William
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internal member
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Advisory Committee
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William Edward Strawderman
Name (ID = NAME-4); (type = personal)
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Singh
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Kesar
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internal member
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Advisory Committee
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Kesar Singh
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Ben-Israel
NamePart (type = given)
Adi
Role
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outside member
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Advisory Committee
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Adi Ben-Israel
Name (ID = NAME-1); (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB); (type = )
degree grantor
Name (ID = NAME-2); (type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm (authority = RULIB); (type = )
school
OriginInfo
DateCreated (point = ); (qualifier = exact)
2009
DateOther (qualifier = exact); (type = degree)
2009-10
Place
PlaceTerm (type = code)
xx
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
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TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/T3XK8FQ5
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

RightsDeclaration (AUTHORITY = GS); (ID = rulibRdec0006)
The author owns the copyright to this work
Copyright
Status
Copyright protected
Notice
Note
Availability
Status
Open
Reason
Permission or license
Note
RightsHolder (ID = PRH-1); (type = personal)
Name
FamilyName
Jiang
GivenName
Wenhua
Role
Copyright holder
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Type
Permission or license
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Place
DateTime
Detail
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Role
Copyright holder
Name
Wenhua Jiang
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject (ID = AO-1); (AUTHORITY = rulib)
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.
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Technical

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ETD
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application/pdf
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application/x-tar
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1966080
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