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PreprintCC BY-NC-ND 4.0HAL

A Kernel Approach to Multivariate Generalized Gammas Convolutions

  • Léo Gonin
  • Esterina Masiello
  • Véronique Maume-Deschamps
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@misc{gonin2026kernel,
  title = {{A Kernel Approach to Multivariate Generalized Gammas Convolutions}},
  author = {Léo Gonin and Esterina Masiello and Véronique Maume-Deschamps},
  howpublished = {HAL},
  year = {2026},
  month = jul,
  doi = {10.48550/arxiv.2609.24681},
  eprint = {2609.24681},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05702801v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - A Kernel Approach to Multivariate Generalized Gammas Convolutions
AU  - Léo Gonin
AU  - Esterina Masiello
AU  - Véronique Maume-Deschamps
PY  - 2026
DA  - 2026/07/23
PB  - HAL
DO  - 10.48550/arxiv.2609.24681
UR  - https://hal.science/hal-05702801v1
AB  - 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.
ER  -