Show simple item record

dc.contributor.advisorDong, Yuexiao
dc.creatorSoale, Abdul-Nasah
dc.date.accessioned2021-05-24T18:45:03Z
dc.date.available2021-05-24T18:45:03Z
dc.date.issued2021
dc.identifier.urihttp://hdl.handle.net/20.500.12613/6488
dc.description.abstractAccompanying the advances in computer technology is an increase collection of high dimensional data in many scientific and social studies. Sufficient dimension reduction (SDR) is a statistical method that enable us to reduce the dimension ofpredictors without loss of regression information. In this dissertation, we introduce principal asymmetric least squares (PALS) as a unified framework for linear and nonlinear sufficient dimension reduction. Classical methods such as sliced inverse regression (Li, 1991) and principal support vector machines (Li, Artemiou and Li, 2011) often do not perform well in the presence of heteroscedastic error, while our proposal addresses this limitation by synthesizing different expectile levels. Through extensive numerical studies, we demonstrate the superior performance of PALS in terms of both computation time and estimation accuracy. For the asymptotic analysis of PALS for linear sufficient dimension reduction, we develop new tools to compute the derivative of an expectation of a non-Lipschitz function. PALS is not designed to handle symmetric link function between the response and the predictors. As a remedy, we develop expectile-assisted inverse regression estimation (EA-IRE) as a unified framework for moment-based inverse regression. We propose to first estimate the expectiles through kernel expectile regression, and then carry out dimension reduction based on random projections of the regression expectiles. Several popular inverse regression methods in the literature including slice inverse regression, slice average variance estimation, and directional regression are extended under this general framework. The proposed expectile-assisted methods outperform existing moment-based dimension reduction methods in both numerical studies and an analysis of the Big Mac data.
dc.format.extent76 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.subjectAsymmetric least squares
dc.subjectExpectile regression
dc.subjectHeteroscedasticity
dc.subjectNonlinear dimension reduction
dc.subjectProjective resampling
dc.subjectSufficient dimension reduction
dc.titleOn Sufficient Dimension Reduction via Asymmetric Least Squares
dc.typeText
dc.type.genreThesis/Dissertation
dc.contributor.committeememberTang, Cheng Yong
dc.contributor.committeememberLee, Kuang-Yao
dc.description.departmentStatistics
dc.relation.doihttp://dx.doi.org/10.34944/dspace/6470
dc.ada.noteFor Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
dc.description.degreePh.D.
dc.identifier.proqst14396
dc.creator.orcid0000-0003-2093-7645
dc.date.updated2021-05-19T16:08:39Z
refterms.dateFOA2021-05-24T18:45:04Z
dc.identifier.filenameSoale_temple_0225E_14396.pdf


Files in this item

Thumbnail
Name:
Soale_temple_0225E_14396.pdf
Size:
609.9Kb
Format:
PDF

This item appears in the following Collection(s)

Show simple item record