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Principal support vector machines for linear and nonlinear sufficient dimension reduction

Li, Bing, Artemiou, Andreas and Li, Lexin 2011. Principal support vector machines for linear and nonlinear sufficient dimension reduction. Annals of Statistics 39 (6) , pp. 3182-3210. 10.1214/11-AOS932

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We introduce a principal support vector machine (PSVM) approach that can be used for both linear and nonlinear sufficient dimension reduction. The basic idea is to divide the response variables into slices and use a modified form of support vector machine to find the optimal hyperplanes that separate them. These optimal hyperplanes are then aligned by the principal components of their normal vectors. It is proved that the aligned normal vectors provide an unbiased, √n-consistent, and asymptotically normal estimator of the sufficient dimension reduction space. The method is then generalized to nonlinear sufficient dimension reduction using the reproducing kernel Hilbert space. In that context, the aligned normal vectors become functions and it is proved that they are unbiased in the sense that they are functions of the true nonlinear sufficient predictors. We compare PSVM with other sufficient dimension reduction methods by simulation and in real data analysis, and through both comparisons firmly establish its practical advantages.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Additional Information: Articles are Open Access 3 years after publication. See [Accessed 14 October 2016]
Publisher: Institute of Mathematical Statistics
ISSN: 0090-5364
Date of First Compliant Deposit: 14 October 2016
Last Modified: 04 Jun 2017 08:20

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