• Login
    View Item 
    •   Home
    • Theses and Dissertations
    • Theses and Dissertations
    • View Item
    •   Home
    • Theses and Dissertations
    • Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of TUScholarShareCommunitiesDateAuthorsTitlesSubjectsGenresThis CollectionDateAuthorsTitlesSubjectsGenres

    My Account

    LoginRegister

    Help

    AboutPeoplePoliciesHelp for DepositorsData DepositFAQs

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    On Sufficient Dimension Reduction via Asymmetric Least Squares

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    Name:
    Soale_temple_0225E_14396.pdf
    Size:
    609.9Kb
    Format:
    PDF
    Download
    Genre
    Thesis/Dissertation
    Date
    2021
    Author
    Soale, Abdul-Nasah cc
    Advisor
    Dong, Yuexiao
    Committee member
    Tang, Cheng Yong
    Lee, Kuang-Yao
    Department
    Statistics
    Subject
    Statistics
    Asymmetric least squares
    Expectile regression
    Heteroscedasticity
    Nonlinear dimension reduction
    Projective resampling
    Sufficient dimension reduction
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/6488
    
    Metadata
    Show full item record
    DOI
    http://dx.doi.org/10.34944/dspace/6470
    Abstract
    Accompanying 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.
    ADA compliance
    For Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
    Collections
    Theses and Dissertations

    entitlement

     
    DSpace software (copyright © 2002 - 2023)  DuraSpace
    Temple University Libraries | 1900 N. 13th Street | Philadelphia, PA 19122
    (215) 204-8212 | scholarshare@temple.edu
    Open Repository is a service operated by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.