Journal of Multivariate Analysis
Journal of Multivariate Analysis
Archimedean copula estimation using Bayesian splines smoothing techniques
Computational Statistics & Data Analysis
Semiparametric bivariate Archimedean copulas
Computational Statistics & Data Analysis
Nonparametric bivariate copula estimation based on shape-restricted support vector regression
Knowledge-Based Systems
Smooth Nonparametric Copula Estimation with Least Squares Support Vector Regression
Neural Processing Letters
Modeling financial dependence with support vector regression
Intelligent Data Analysis
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A new multivariate Archimedean copula estimation method is proposed in a non-parametric setting. The method uses the so-called Geometrically Designed splines (GeD splines) to represent the cdf of a random variable W"@q, obtained through the probability integral transform of an Archimedean copula with parameter @q. Sufficient conditions for the GeD spline estimator to possess the properties of the underlying theoretical cdf, K(@q,t), of W"@q, are given. The latter conditions allow for defining a three-step estimation procedure for solving the resulting non-linear regression problem with linear inequality constraints. In the proposed procedure, finding the number and location of the knots and the coefficients of the unconstrained GeD spline estimator and solving the constraint least-squares optimisation problem are separated. Thus, the resulting spline estimator K@?(@q@?,t) is used to recover the generator and the related Archimedean copula by solving an ordinary differential equation. The proposed method is truly multivariate, it brings about numerical efficiency and as a result can be applied with large volumes of data and for dimensions d=2, as illustrated by the numerical examples presented.