Constraints on concordance measures in bivariate discrete data
Journal of Multivariate Analysis
Computational Statistics & Data Analysis
Generalized structured additive regression based on Bayesian P-splines
Computational Statistics & Data Analysis
GeD spline estimation of multivariate Archimedean copulas
Computational Statistics & Data Analysis
Bayesian density estimation from grouped continuous data
Computational Statistics & Data Analysis
Semiparametric bivariate Archimedean copulas
Computational Statistics & Data Analysis
Copula density estimation by total variation penalized likelihood with linear equality constraints
Computational Statistics & Data Analysis
Journal of Multivariate 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
Penalized marginal likelihood estimation of finite mixtures of Archimedean copulas
Computational Statistics
Modeling financial dependence with support vector regression
Intelligent Data Analysis
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Copulas enable to specify multivariate distributions with given marginals. Various parametric proposals were made in the literature for these quantities, mainly in the bivariate case. They can be systematically derived from multivariate distributions with known marginals, yielding e.g. the normal and the Student copulas. Alternatively, one can restrict his/her interest to a sub-family of copulas named Archimedean. They are characterized by a strictly decreasing convex function on (0,1) which tends to +~ at 0 (when strict) and which is 0 at 1. A ratio approximation of the generator and of its first derivative using B-splines is proposed and the associated parameters estimated using Markov chains Monte Carlo methods. The estimation is reasonably quick. The fitted generator is smooth and parametric. The generated chain(s) can be used to build ''credible envelopes'' for the above ratio function and derived quantities such as Kendall's tau, posterior predictive probabilities, etc. Parameters associated to parametric models for the marginals can be estimated jointly with the copula parameters. This is an interesting alternative to the popular two-step procedure which assumes that the regression parameters are fixed known quantities when it comes to copula parameter(s) estimation. A simulation study is performed to evaluate the approach. The practical utility of the method is illustrated by a basic analysis of the dependence structure underlying the diastolic and the systolic blood pressures in male subjects.