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dc.contributor.advisorDong, Yuexiao
dc.contributor.advisorTang, Cheng-Yong
dc.creatorXIA, QI
dc.date.accessioned2020-11-05T16:15:46Z
dc.date.available2020-11-05T16:15:46Z
dc.date.issued2017
dc.identifier.urihttp://hdl.handle.net/20.500.12613/3859
dc.description.abstractExisting sufficient dimension reduction (SDR) methods typically consider cases with no missing data. The dissertation aims to propose methods to facilitate the SDR methods when the response can be missing. The first part of the dissertation focuses on the seminal sliced inverse regression (SIR) approach proposed by Li (1991). We show that missing responses generally affect the validity of the inverse regressions under the mechanism of missing at random. We then propose a simple and effective adjustment with inverse probability weighting that guarantees the validity of SIR. Furthermore, a marginal coordinate test is introduced for this adjusted estimator. The proposed method share the simplicity of SIR and requires the linear conditional mean assumption. The second part of the dissertation proposes two new estimating equation procedures: the complete case estimating equation approach and the inverse probability weighted estimating equation approach. The two approaches are applied to a family of dimension reduction methods, which includes ordinary least squares, principal Hessian directions, and SIR. By solving the estimating equations, the two approaches are able to avoid the common assumptions in the SDR literature, the linear conditional mean assumption, and the constant conditional variance assumption. For all the aforementioned methods, the asymptotic properties are established, and their superb finite sample performances are demonstrated through extensive numerical studies as well as a real data analysis. In addition, existing estimators of the central mean space have uneven performances across different types of link functions. To address this limitation, a new hybrid SDR estimator is proposed that successfully recovers the central mean space for a wide range of link functions. Based on the new hybrid estimator, we further study the order determination procedure and the marginal coordinate test. The superior performance of the hybrid estimator over existing methods is demonstrated in simulation studies. Note that the proposed procedures dealing with the missing response at random can be simply adapted to this hybrid method.
dc.format.extent143 pages
dc.language.isoeng
dc.publisherTemple University. Libraries
dc.relation.ispartofTheses and Dissertations
dc.rightsIN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available.
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectStatistics
dc.subjectMissing at Random
dc.subjectOrdinary Least Squares
dc.subjectPrincipal Hessian Directions
dc.subjectSliced Inverse Regression
dc.subjectSufficient Dimension Reduction
dc.titleSufficient Dimension Reduction with Missing Data
dc.typeText
dc.type.genreThesis/Dissertation
dc.contributor.committeememberWei, William W. S.
dc.contributor.committeememberHan, Xu
dc.contributor.committeememberYang, Yang
dc.description.departmentStatistics
dc.relation.doihttp://dx.doi.org/10.34944/dspace/3841
dc.ada.noteFor Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
dc.description.degreePh.D.
refterms.dateFOA2020-11-05T16:15:46Z


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