Erhardt and Czado (2008) suggest an approximative method for sampling highdimensional count random variables with a specified Pearson correlation. They utilize Gaussian copulae for the construction of multivariate discrete distributions. A major task is to determine the appropriate copula parameters for the achievement of a specified target correlation. Erhardt and Czado (2008) develop an optim...

We examine the standard Gaussian copula model for correlated defaults (also called the survival copula) and its relationship with the theoretically richer model based on diffusion processes and default thresholds. We show that in a discrete time framework the Gaussian copula can be seen as a simple global approximation to the Brownian copula implied by correlated diffusions. More precisely, the...

The authors extend to multivariate contexts the copula-based univariate time series modeling approach of Chen & Fan [X. Chen, Y. Fan, Estimation of copula-based semiparametric time series models, J. Econometrics 130 (2006) 307–335; X. Chen, Y. Fan, Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification, J. Econometrics 135 (2006) ...

For a multivariate vector X with discrete components, we construct, by means of explicit randomised transformations of X, multivariate couplings of copula representers U associated to X. As a result, we show that any copula can be constructed in this manner, giving a full probabilistic characterisation of the set of copula functions associated to X. The dependence properties of these copula rep...

The Vale-Maurelli (VM) approach to generating non-normal multivariate data involves the use of Fleishman polynomials applied to an underlying Gaussian random vector. This method has been extensively used in Monte Carlo studies during the last three decades to investigate the finite-sample performance of estimators under non-Gaussian conditions. The validity of conclusions drawn from these studi...

Copula functions have been extensively used to describe the joint behaviors of extreme hydrological events and to analyze hydrological risk. Advanced marginal distribution inference, for example, the maximum entropy theory, is particularly beneficial for improving the performance of the copulas. The goal of this paper, therefore, is twofold; first, to develop a coupled maximum entropy-copula me...

We propose a comprehensive Bayesian approach for graphical model determination in observational studies that can accommodate binary, ordinal or continuous variables simultaneously. Our new models are called copula Gaussian graphical models and embed graphical model selection inside a semiparametric Gaussian copula. The domain of applicability of our methods is very broad and encompass many stud...

We clarify the link between the notion of singular copula and the concept of support of the measure induced by a copula.