Inference for Hüsler-Reiss block models
Abstract
Estimating the Hüsler-Reiss precision matrix is a fundamental problem for statistical inference in multivariate extremes. In high-dimensional settings, the number of unknown parameters grows quadratically with the dimension, making regularisation indispensable. Existing approaches regularise the estimation problem by exploiting sparsity. In this paper, we consider an alternative structural assumption, namely that the Hüsler-Reiss precision matrix is block-structured. To estimate such a matrix, we introduce a new regularisation framework based on a convex fusion penalty. By encouraging rows and columns to merge, this approach provides a parsimonious representation of the precision matrix, allowing for the simultaneous estimation of its coefficients and the underlying partition of the variables. The resulting convex optimisation problem is solved by an efficient algorithm combining gradient-based updates with progressive fusion steps. We establish non-asymptotic concentration bounds for the empirical weights entering the penalty and prove consistency of both block recovery and precision matrix estimation under suitable regularity conditions. Numerical experiments demonstrate that our methodology accurately recovers the latent block structure while accurately estimating the Hüsler-Reiss precision matrix across various configurations, illustrating the practical benefits of fusion-based regularisation for multivariate extremes. These benefits are also demonstrated by applying the proposed method to foreign exchange data.
Related
- Block Designs with Large Transversal-Block Intersections
- Block-count constrained harmonic sums: spectral expansion and block-directed Euler-Maclaurin
- Block Toeplitz Operators, Matrix Valued Truncated Toeplitz operators, and Conjugations
- Local and 2-local derivations of Block Lie algebras B(q)
- A Note on the Drazin Inverse of 2 × 2 Block Triangular Matrices
BibTeX
@misc{capel2026inference,
title = {{Inference for Hüsler-Reiss block models}},
author = {Alexandre Capel and Nicolas Meyer and Marine Demangeot and Gwladys Toulemonde},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26501},
eprint = {2609.26501},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05755237v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Inference for Hüsler-Reiss block models
AU - Alexandre Capel
AU - Nicolas Meyer
AU - Marine Demangeot
AU - Gwladys Toulemonde
PY - 2026
DA - 2026/09/18
PB - HAL
DO - 10.48550/arxiv.2609.26501
UR - https://hal.science/hal-05755237v1
AB - Estimating the Hüsler-Reiss precision matrix is a fundamental problem for statistical inference in multivariate extremes. In high-dimensional settings, the number of unknown parameters grows quadratically with the dimension, making regularisation indispensable. Existing approaches regularise the estimation problem by exploiting sparsity. In this paper, we consider an alternative structural assumption, namely that the Hüsler-Reiss precision matrix is block-structured. To estimate such a matrix, we introduce a new regularisation framework based on a convex fusion penalty. By encouraging rows and columns to merge, this approach provides a parsimonious representation of the precision matrix, allowing for the simultaneous estimation of its coefficients and the underlying partition of the variables. The resulting convex optimisation problem is solved by an efficient algorithm combining gradient-based updates with progressive fusion steps. We establish non-asymptotic concentration bounds for the empirical weights entering the penalty and prove consistency of both block recovery and precision matrix estimation under suitable regularity conditions. Numerical experiments demonstrate that our methodology accurately recovers the latent block structure while accurately estimating the Hüsler-Reiss precision matrix across various configurations, illustrating the practical benefits of fusion-based regularisation for multivariate extremes. These benefits are also demonstrated by applying the proposed method to foreign exchange data.
ER -