Least Squares Support Vector Machine Classifiers
Neural Processing Letters
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Primal-Dual Monotone Kernel Regression
Neural Processing Letters
An Introduction to Copulas (Springer Series in Statistics)
An Introduction to Copulas (Springer Series in Statistics)
Nonparametric Quantile Estimation
The Journal of Machine Learning Research
Archimedean copula estimation using Bayesian splines smoothing techniques
Computational Statistics & Data Analysis
The Black Swan: The Impact of the Highly Improbable
The Black Swan: The Impact of the Highly Improbable
Incorporating prior knowledge in support vector regression
Machine Learning
GeD spline estimation of multivariate Archimedean copulas
Computational Statistics & Data Analysis
Linear B-spline copulas with applications to nonparametric estimation of copulas
Computational Statistics & Data Analysis
Thresholding methods to estimate copula density
Journal of Multivariate Analysis
Cutting plane method for continuously constrained kernel-based regression
IEEE Transactions on Neural Networks
Nonlinear Knowledge in Kernel Approximation
IEEE Transactions on Neural Networks
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Copula has become the standard tool in financial dependence modeling. This paper proposes a novel nonparametric bivariate copula estimation method which smooths empirical copula with shape-restricted least squares support vector regression. This method exploits a priori shape knowledge of copula function: boundary and 2-increasing, by supplementing the classical support vector regression with shape-related constraints on an equidistant grid of the support [0,1]^2. Its training can be reformulated to a convex quadratic program, which is computationally tractable. Experiments on both an artificial data set and financial time series clearly show that it has good finite sample property and can achieve significantly better performance than parametric methods and kernel smoother.