Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 10, Number 1 (2016), 783-805.
Sufficient dimension reduction via principal L$q$ support vector machine
Principal support vector machine was proposed recently by Li, Artemiou and Li (2011) to combine L1 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 L1 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 L2 support vector machine estimators improve existing methods in accuracy, and are less sensitive to the tuning parameter selection.
Electron. J. Statist., Volume 10, Number 1 (2016), 783-805.
Received: August 2014
First available in Project Euclid: 6 April 2016
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Artemiou, Andreas; Dong, Yuexiao. Sufficient dimension reduction via principal L$q$ support vector machine. Electron. J. Statist. 10 (2016), no. 1, 783--805. doi:10.1214/16-EJS1122. https://projecteuclid.org/euclid.ejs/1459967423