Modeling multivariate extreme value distributions via Markov trees

Shuang Hu, Zuoxiang Peng and Johan Segers ()
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Johan Segers: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2023031, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: Multivariate extreme value distributions are a common choice for modeling multivariate extremes. In high dimensions, however, the construction of flexible and parsimonious models is challenging. We propose to combine bivariate max-stable distributions into a Markov random field with respect to a tree. Although in general not max-stable itself, this Markov tree is attracted by a multivariate max-stable distribution. The latter serves as a tree-based approximation to an unknown max-stable distribution with the given bivariate distributions as margins. Given data, we learn an appropriate tree structure by Prim's algorithm with estimated pairwise upper tail dependence coefficients as edge weights. The distributions of pairs of connected variables can be fitted in various ways. The resulting tree-structured max-stable distribution allows for inference on rare event probabilities, as illustrated on river discharge data from the upper Danube basin.

Keywords: Kendall’s tau; Markov tree; Multivariate extreme value distribution; Prim’s algorithm; probabilistic graphical model; rare event; tail dependence (search for similar items in EconPapers)
Pages: 41
Date: 2023-11-30
Note: In: Scandinavian Journal of Statistics, 2024
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2023031

DOI: 10.1111/sjos.12698

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