文章基本信息

标题：Sufficient dimension reduction via principal L$q$ support vector machine
本地全文：下载
作者：Andreas Artemiou ; Yuexiao Dong
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2016
卷号：10
期号：1
页码：783-805
DOI：10.1214/16-EJS1122
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.