arXiv subjects

Esterina Masiello

Publications and source records attributed to Esterina Masiello.

3 recordsLinked to original sources

arXiv2026

A Kernel Approach to Multivariate Generalized Gammas Convolutions

We propose a kernel-based estimation framework for Multivariate Generalized Gamma convolutions (MGGC), a class of probability distributions on R d + . MGGC are useful for risk modeling e.g. Their densities are in general not explicit. The construction relies on a new Stein operator for the MGGC class, derived from a partial differential equation satisfied by the characteristic function and expressed as an integral against the underlying Thorin measure. This leads to construct a new kernel and an estimation procedure in the derived reproducing kernel Hilbert space (RKHS); with consistency results. Numerical experiments illustrate the practical behaviour of the proposed estimator.

math.PR↗

arXiv2021

Estimation of multivariate generalized gamma convolutions through Laguerre expansions

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.

math.ST↗

arXiv2021

Dependence structure estimation using Copula Recursive Trees

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.

math.ST↗