The generalized gamma convolutions class of distributions appeared in Thorin's work while looking for the infinite divisibility of the log-Normal and Pareto distributions. Although these distributions have been extensively studied in the univariate case, the multivariate case and the dependence structures that can arise from it have received little interest in the literature. Furthermore, only one projection procedure for the univariate case was recently constructed, and no estimation procedures are available. By expanding the densities of multivariate generalized gamma convolutions into a tensorized Laguerre basis, we bridge the gap and provide performant estimation procedures for both the univariate and multivariate cases. We provide some insights about performance of these procedures, and a convergent series for the density of multivariate gamma convolutions, which is shown to be more stable than Moschopoulos's and Mathai's univariate series. We furthermore discuss some examples.

We construct the COpula Recursive Tree (CORT) estimator: a flexible, consistent, piecewise linear estimator of a copula, leveraging the patchwork copula formalization and various piecewise constant density estimators. While the patchwork structure imposes a grid, the CORT estimator is data-driven and constructs the (possibly irregular) grid recursively from the data, minimizing a chosen distance on the copula space. The addition of the copula constraints makes usual density estimators unusable, whereas the CORT estimator is only concerned with dependence and guarantees the uniformity of margins. Refinements such as localized dimension reduction and bagging are developed, analyzed, and tested through simulated data.

No abstract

The generalized gamma convolution class of distribution appeared in Thorin's work while looking for the infinite divisibility of the log-Normal and Pareto distributions. Although these distributions have been extensively studied in the univariate case, the multivariate case and the dependence structures that can arise from it have received little interest in the literature. Furthermore, only one projection procedure for the univariate case was recently constructed, and no estimation procedure are available. By expending the densities of multivariate generalized gamma convolutions into a tensorized Laguerre basis, we bridge the gap and provide performant estimations procedures for both the univariate and multivariate cases. We provide some insights about performance of these procedures, and a convergent series for the density of multivariate gamma convolutions, which is shown to be more stable than Moschopoulos's and Mathai's univariate series. We furthermore discuss some examples.