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    Bayesian Model Averaging Sufficient Dimension Reduction

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    Genre
    Thesis/Dissertation
    Date
    2020
    Author
    Power, Michael Declan
    Advisor
    Dong, Yuexiao
    Committee member
    Zhao, Zhigen
    Lee, Kuang-Yao
    Frey, Jesse
    Department
    Statistics
    Subject
    Statistics
    Bayesian Model Averaging
    Distance Correlation
    Principal Hessian Directions
    Sliced Inverse Regression
    Sufficient Dimension Reduction
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/3421
    
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    DOI
    http://dx.doi.org/10.34944/dspace/3403
    Abstract
    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.
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