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Bayesian Model Averaging Sufficient Dimension Reduction

In sufficient dimension reduction (Li, 1991; Cook, 1998b), original predictors are replaced by their low-dimensional linear combinations while preserving all of the conditional information of the response given the predictors. Sliced inverse regression [SIR; Li, 1991] and principal Hessian directions [PHD; Li, 1992] are two popular sufficient dimension reduction methods, and both SIR and PHD estimators involve all of the original predictor variables. To deal with the cases when the linear combinations involve only a subset of the original predictors, we propose a Bayesian model averaging (Raftery et al., 1997) approach to achieve sparse sufficient dimension reduction. We extend both SIR and PHD under the Bayesian framework. The superior performance of the proposed methods is demonstrated through extensive numerical studies as well as a real data analysis. / Statistics

Identiferoai:union.ndltd.org:TEMPLE/oai:scholarshare.temple.edu:20.500.12613/3421
Date January 2020
CreatorsPower, Michael Declan
ContributorsDong, Yuexiao, Zhao, Zhigen, Lee, Kuang-Yao, Frey, Jesse
PublisherTemple University. Libraries
Source SetsTemple University
LanguageEnglish
Detected LanguageEnglish
TypeThesis/Dissertation, Text
Format56 pages
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Relationhttp://dx.doi.org/10.34944/dspace/3403, Theses and Dissertations

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