Oracle properties of SCAD-penalized support vector machine

Changyi Park, Kwang Rae Kim, Rangmi Myung, Ja Yong Koo

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)2257-2270
Number of pages14
JournalJournal of Statistical Planning and Inference
Volume142
Issue number8
DOIs
StatePublished - Aug 2012

Keywords

  • Classification
  • Fisher consistency
  • Oracle property
  • Smoothly clipped absolute deviation

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