Smooth Nonparametric Copula Estimation with Least Squares Support Vector Regression

Copula has become the standard tool in dependence modeling. With the aide of copula, the estimation of multivariate distributions can be obtained by two steps: marginal distributions construction and copula estimation. This paper puts forward a smooth nonparametric copula estimation based on least squares support vector regression. By supplementing the classical least squares support vector regression with some additional shape-related constraints, this method tries to make the estimator satisfy three shape restrictions of copula: grounded, marginal and 2-increasing. Its training involves a simple convex quadratic programming problem, which can be solved in polynomial time. Experimental results clearly showed that this method could achieve significantly better performance than the classical least squares support vector regression and kernel smoother for copula estimation.

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