Statistical Inference for Hüsler–Reiss Graphical Models Through Matrix Completions

Manuel Hentschel, Sebastian Engelke and Johan Segers ()
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Manuel Hentschel: University of Geneva
Sebastian Engelke: University of Geneva
Johan Segers: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2024019, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: The severity of multivariate extreme events is driven by the dependence between the largest marginal observations. The Hüsler–Reiss distribution is a versatile model for this extremal dependence, and it is usually parameterized by a variogram matrix. In order to represent conditional independence relations and obtain sparse parameterizations, we introduce the novel Hüsler–Reiss precision matrix. Similarly to the Gaussian case, this matrix appears naturally in density representations of the Hüsler–Reiss Pareto distribution and encodes the extremal graphical structure through its zero pattern. For a given, arbitrary graph we prove the existence and uniqueness of the completion of a partially specified Hüsler–Reiss variogram matrix so that its precision matrix has zeros on non-edges in the graph. Using suitable estimators for the parameters on the edges, our theory provides the first consistent estimator of graph structured Hüsler–Reiss distributions. If the graph is unknown, our method can be combined with recent structure learning algorithms to jointly infer the graph and the corresponding parameter matrix. Based on our methodology, we propose new tools for statistical inference of sparse Hüsler–Reiss models and illustrate them on large flight delay data in the U.S., as well as Danube river flow data.

Keywords: Extreme value analysis; multivariate generalized Pareto distribution; sparsity; variogram (search for similar items in EconPapers)
Pages: 40
Date: 2024-06-26
Note: In: Journal of the American Statistical Association, 2024
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2024019

DOI: 10.1080/01621459.2024.2371978

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