The Asymptotic Statistical Properties Of Support Vector Machines And Its Application

In this paper, we have mostly discussed the asymptotic statistical properties of support vector machines. Firstly, we introduce the support vector machines and some related concepts, then analyze the present situation of research. Secondly, we define the average generalization error of single variable weighted support vector machines E(|θL-θR|/2π) on the basis of sample transformation Thirdly, in the situation that the sample size and the number of support vectors are sufficiently large, we study the asymptotic distribution of θL - θR, and get the upper bound of average generalization error. Then, we select three common weights: equal weight, fractional weight and index weight, and calculate the average generalization of them. The result of random data simulation is consistent with the theoretical conclusion.In addition, we combine the statistical modeling methods with support vector machines,and carry on the instance analysis in the field of quantitative investment.Based on the 2007-2015,nine years, daily data of Shanghai composite index, we use variable selection and parameter selection to build a classification prediction model, with support vector machines as the core. This model has achieved good results.