Oracle properties of SCAD-penalized support vector machine

详细信息	查看全文 | 推荐本文 |

• 作者：Changyi Park^a ; Kwang-Rae Kim^b ; ^{linuxerk@korea.ac.kr} ; Rangmi Myung^c ; Ja-Yong Koo^d
• 关键词：Classification ; Fisher consistency ; Oracle property ; Smoothly clipped absolute deviation
• 刊名：Journal of Statistical Planning and Inference
• 出版年：2012
• 期刊代码：36_03783758
• 类别：mt
• 出版时间：August, 2012
• 卷：142
• 期：8
• 页码：2257-2270
• 文件大小：284 K

摘要

In many scientific investigations, a large number of input variables are given at the early stage of modeling and identifying the variables predictive of the response is often a main purpose of such investigations. Recently, the support vector machine has become an important tool in classification problems of many fields. Several variants of the support vector machine adopting different penalties in its objective function have been proposed. This paper deals with the Fisher consistency and the oracle property of support vector machines in the setting where the dimension of inputs is fixed. First, we study the Fisher consistency of the support vector machine over the class of affine functions. It is shown that the function class for decision functions is crucial for the Fisher consistency. Second, we study the oracle property of the penalized support vector machines with the smoothly clipped absolute deviation penalty. Once we have addressed the Fisher consistency of the support vector machine over the class of affine functions, the oracle property appears to be meaningful in the context of classification. A simulation study is provided in order to show small sample properties of the penalized support vector machines with the smoothly clipped absolute deviation penalty.