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Abstract Details
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Activity Number:
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39
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Type:
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Contributed
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Date/Time:
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Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
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Sponsor:
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IMS
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| Abstract - #301471 |
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Title:
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Nonlinear Sufficient Dimension Reduction Using Reproducing Kernel Hilbert Space
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Author(s):
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Kuang-Yao Lee*+ and Bing Li and Francesca Chiaromonte
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Companies:
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Penn State University and Penn State University and Penn State University
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Address:
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, State College, PA, 16802,
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Keywords:
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sufficient dimension reduction ;
nonlinearity ;
reproducing kernel Hilbert space ;
sliced inverse regression
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Abstract:
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We introduce a novel framework for nonlinear sufficient dimension reduction. Classical sufficient dimension reduction (SDR) aims at searching directions in a Euclidean space that can preserve adequate information about the relation between a vector-valued predictor and a response. We reformulate SDR in a nonlinear setting where the effective predictors are allowed to be arbitrary functions. Two main issues will be discussed. The first is the theoretical formulation and characterization of sufficiency for supervised nonlinear reduction reduction. The second is to develop procedures for unbiased and/or exhaustive estimation of the sufficient nonlinear dimension reduction space. We will also study several existing procedures for nonlinear dimension reduction in the light of this new framework. Some applications and simulation results will be presented.
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