RUcore: Rutgers University Community Repository
Nonparametric and semiparametric regression, missing data, and related algorithms
Descriptive
TypeOfResource
Text
TitleInfo
(ID = T-1)
Title
Nonparametric and semiparametric regression, missing data, and related algorithms
SubTitle
PartName
PartNumber
NonSort
Identifier
(displayLabel = );
(invalid = )
ETD_2272
Identifier
(type = hdl)
http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000052210
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
Nonparametric statistics
Subject
(ID = SBJ-3);
(authority = ETD-LCSH)
Topic
Regression analysis
Abstract
This dissertation consists of two chapters: Chapter 1 develops nonparametric and semiparametric regression methodologies which relate the group testing responses to the individual covariates information. In this chapter, we extend the parametric regression model of Xie (2001) for binary group testing data to the nonparametric and semiparametric models. We fit nonparametric and semiparametric models and obtain estimators of the parameters by maximizing penalized likelihood function. For implementation, we apply EM algorithm considering the individual responses as complete data and the group testing responses as observed data. Simulation studies are performed to illustrate the methodologies and to evaluate the finite sample performance of our methods. In general, group testing involves a large number of subjects, hence, the computational aspect is also discussed. The results show that our estimation methods perform well for estimating both the individual probability of positive outcome and the prevalence rate in the population.
Chapter 2 studies a partially linear regression model with missing response variable and develops semiparametric efficient inference for the parametric component of the model. The missingness considered here includes a broad range of missing patterns. For the estimation method, we use the concept of least favorable curve, least favorable direction and the generalized profile likelihood in Severini and Wong (1992). Asymptotic distributions for the estimators of the parametric components are obtained. It is shown that the estimators are asymptotically normally distributed under some conditions. Furthermore, we prove that the asymptotic covariance of the estimators achieves the semiparametric lower bound under the regularity conditions and additional conditions given in the appendix.
We also propose an algorithm which runs iteratively between fitting parametric components and fitting nonparametric components while holding the other fixed. EM algorithms are used in estimating the parametric components by a semiparametric estimating equation and in estimating the nonparametric components by smoothing methods. It is proved that the estimators from this iterative algorithm equal to the conditional expectations (conditioned on observed data) of the semiparametric efficient estimators from complete data. The methodology is illustrated and evaluated by numerical examples.
Chapter 2 studies a partially linear regression model with missing response variable and develops semiparametric efficient inference for the parametric component of the model. The missingness considered here includes a broad range of missing patterns. For the estimation method, we use the concept of least favorable curve, least favorable direction and the generalized profile likelihood in Severini and Wong (1992). Asymptotic distributions for the estimators of the parametric components are obtained. It is shown that the estimators are asymptotically normally distributed under some conditions. Furthermore, we prove that the asymptotic covariance of the estimators achieves the semiparametric lower bound under the regularity conditions and additional conditions given in the appendix.
We also propose an algorithm which runs iteratively between fitting parametric components and fitting nonparametric components while holding the other fixed. EM algorithms are used in estimating the parametric components by a semiparametric estimating equation and in estimating the nonparametric components by smoothing methods. It is proved that the estimators from this iterative algorithm equal to the conditional expectations (conditioned on observed data) of the semiparametric efficient estimators from complete data. The methodology is illustrated and evaluated by numerical examples.
PhysicalDescription
Form
(authority = gmd)
electronic resource
Extent
vii, 59 p. : ill.
InternetMediaType
application/pdf
InternetMediaType
text/xml
Note
(type = degree)
Ph.D.
Note
(type = bibliography)
Includes bibliographical references
Note
(type = statement of responsibility)
by Mingyu Li
Name
(ID = NAME-1);
(type = personal)
NamePart
(type = family)
Li
NamePart
(type = given)
Mingyu
NamePart
(type = date)
1981-
Role
RoleTerm
(authority = RULIB);
(type = )
author
DisplayForm
Mingyu Li
Name
(ID = NAME-2);
(type = personal)
NamePart
(type = family)
Xie
NamePart
(type = given)
Minge
Role
RoleTerm
(authority = RULIB);
(type = )
chair
Affiliation
Advisory Committee
DisplayForm
Minge Xie
Name
(ID = NAME-3);
(type = personal)
NamePart
(type = family)
Kolassa
NamePart
(type = given)
John
Role
RoleTerm
(authority = RULIB);
(type = )
internal member
Affiliation
Advisory Committee
DisplayForm
John Kolassa
Name
(ID = NAME-4);
(type = personal)
NamePart
(type = family)
Singh
NamePart
(type = given)
Kesar
Role
RoleTerm
(authority = RULIB);
(type = )
internal member
Affiliation
Advisory Committee
DisplayForm
Kesar Singh
Name
(ID = NAME-5);
(type = personal)
NamePart
(type = family)
Huang
NamePart
(type = given)
Tao
Role
RoleTerm
(authority = RULIB);
(type = )
outside member
Affiliation
Advisory Committee
DisplayForm
Tao Huang
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)
2010
DateOther
(qualifier = exact);
(type = degree)
2010-01
Place
PlaceTerm
(type = code)
xx
RelatedItem
(type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier
(type = RULIB)
ETD
RelatedItem
(type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier
(type = local)
rucore19991600001
Location
PhysicalLocation
(authority = marcorg);
(displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier
(type = doi)
doi:10.7282/T30Z73D1
Genre
(authority = ExL-Esploro)
ETD doctoral
Back to the top
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
Li
GivenName
Mingyu
Role
Copyright Holder
RightsEvent
(ID = RE-1);
(AUTHORITY = rulib)
Type
Permission or license
Label
Place
DateTime
2009-12-03 17:04:30
Detail
AssociatedEntity
(ID = AE-1);
(AUTHORITY = rulib)
Role
Copyright holder
Name
Mingyu Li
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.
Back to the top
Technical
ContentModel
ETD
MimeType
(TYPE = file)
application/pdf
MimeType
(TYPE = container)
application/x-tar
FileSize
(UNIT = bytes)
3225600
Checksum
(METHOD = SHA1)
f38c1dfb31285b50a94f9b63d980b189bfd5d64a
Back to the top
Statistical Profile