In this dissertation we introduce two variable selection procedures for multivariate responses. Our procedures are based on sufficient dimension reduction concepts and are model-free. In the first procedure we consider the dual marginal coordinate hypotheses, where the role of the predictor and the response is not important. Motivated by canonical correlation analysis (CCA), we propose a CCA-based test for the dual marginal coordinate hypotheses, and devise a joint backward selection algorithm for dual model-free variable selection. The second procedure is based on ordinary least squares (OLS). We derive and study the asymptotic properties of the OLS-based test under the normality assumption of the predictors as well as an asymmetry assumption. When these assumptions are violated, the asymptotic test with elliptical trimming and clustering is still valid with desirable numerical performances. A backward selection algorithm for the predictor is also provided for the OLS-based test. The performances of the proposed tests and the variable selection procedures are evaluated through synthetic examples and a real data analysis. / Statistics
| Identifer | oai:union.ndltd.org:TEMPLE/oai:scholarshare.temple.edu:20.500.12613/675 |
| Date | January 2018 |
| Creators | Alothman, Ahmad |
| Contributors | Dong, Yuexiao, Tang, Cheng Yong, Chitturi, Pallavi, Shen, Cencheng |
| Publisher | Temple University. Libraries |
| Source Sets | Temple University |
| Language | English |
| Detected Language | English |
| Type | Thesis/Dissertation, Text |
| Format | 79 pages |
| Rights | IN 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., http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | http://dx.doi.org/10.34944/dspace/657, Theses and Dissertations |
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