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Activity Number:
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220
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Type:
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Contributed
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Date/Time:
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Monday, August 3, 2009 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Nonparametric Statistics
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| Abstract - #303893 |
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Title:
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Nonparametric Regression Analysis of SPD Matrices
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Author(s):
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Ying Yuan*+ and Hongtu Zhu and J. Steve Marron and Dinggang Shen
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Companies:
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The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill
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Address:
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Department of Statistics, Chapel Hill, NC, 27514,
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Keywords:
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Riemannian manifold ; nonparametric regression ; symmetric positive definite matrix ; bootstrap bandwidth selection
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Abstract:
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The study of the unknown relationship between symmetric positive-definite (SPD) matrices as a response and a set of covariates in the Euclidean space is gaining interest in practice, e.g. in investigating the variation of the diffusion tensors along the fiber tract in the brain or studying the effect of age on the brain (connectivity) network, in medical imaging research. In addition, because SPD matrices do not form a vector space instead of a non-Euclidean space, applying the classical multivariate nonparametric methods to modeling SPD matrices may undermine their association with covariates of interest. In response, this dissertation is devoted to the development of a nonparametric regression framework for analyzing SPD matrices by taking account of the fact that SPD matrices forms a non-Euclidean Euclidean space.
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