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Sufficient dimension reduction via principal Lq support vector machine

Artemiou, Andreas and Dong, Yuexiao 2016. Sufficient dimension reduction via principal Lq support vector machine. Electronic Journal of Statistics 10 (1) , pp. 783-805. 10.1214/154957804100000000

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Abstract

Principal support vector machine was proposed recently by Li, Artemiou and Li (2011) to combine L$1$ support vector machine and sufficient dimension reduction. We introduce the principal L$q$ support vector machine as a unified framework for linear and nonlinear sufficient dimension reduction. By noticing that the solution of L$1$ support vector machine may not be unique, we set $q>1$ to ensure the uniqueness of the solution. The asymptotic distribution of the proposed estimators are derived for $q> 1$. We demonstrate through numerical studies that the proposed L$2$ support vector machine estimators improve existing methods in accuracy, and are less sensitive to the tuning parameter selection.

Item Type: Article
Date Type: Published Online
Status: Published
Schools: Advanced Research Computing @ Cardiff (ARCCA)
Mathematics
Subjects: Q Science > QA Mathematics
Additional Information: Pdf uploaded in accordance with publisher's policy at http://www.sherpa.ac.uk/romeo/issn/1935-7524/ (accessed 29/03/2016)
Publisher: Institute of Mathematical Statistics
ISSN: 1935-7524
Date of First Compliant Deposit: 30 March 2016
Date of Acceptance: 20 February 2016
Last Modified: 04 Jun 2017 18:28
URI: http://orca.cf.ac.uk/id/eprint/88308

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