Sufficient Dimension Reduction via Principal Lq Support Vector Machine

• Activity Number: 57
• Type: Topic Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yuexiao Dong*+ and Andreas Artemiou
• Companies: Temple University and Cardiff University
• Keywords: Inverse regression ; L2 support vector machine ; Reproducing kernel Hilbert space

Abstract

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 Lq 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 = 2. 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.