A Bahadur representation of the linear support vector machine

The support vector machine has been successful in a variety of applications. Also on the theoretical front, statistical properties of the support vector machine have been studied quite extensively with a particular attention to its Bayes risk consistency under some conditions. In this paper, we study somewhat basic statistical properties of the support vector machine yet to be investigated, namely the asymptotic behavior of the coefficients of the linear support vector machine. A Bahadur type representation of the coefficients is established under appropriate conditions, and their asymptotic normality and statistical variability are derived on the basis of the representation. These asymptotic results do not only help further our understanding of the support vector machine, but also they can be useful for related statistical inferences.