Support Vector Machine Method for Multivariate Density Estimation Based on Copulas

In this paper, a new method for estimating multivariate density functions is proposed based on Support Vector Machine (SVM) technique and copulas. It is well-known that the SVM method can result in a sparse and accurate estimate of a density function, however, the knowledge of marginal densities of a multivariate density are not employed directly although they may be known in some applications such as multi-sensor systems. Benefitted from Sklar´s theorem, in which a joint distribution function is characterized by its margins through a copula, the proposed approach can incorporate efficiently the knowledge of the margins and dependence structure of random samples into density estimation so that more accurate estimates are obtained. Some numerical examples are given to demonstrate that our approach can result in more accurate estimates than both direct SVM method and multivariate kernel density method based on copulas.