Modeling multivariate extreme value distributions via Markov trees

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 tre...

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Bibliographic Details
Published in:Scandinavian journal of statistics 2024-06, Vol.51 (2), p.760-800
Main Authors: Hu, Shuang, Peng, Zuoxiang, Segers, Johan
Format: Article
Language:English
Subjects:
Algorithms
Bivariate analysis
Extreme values
Fields (mathematics)
Kendall's tau
Markov tree
Modelling
Multivariate analysis
multivariate extreme value distribution
Prim's algorithm
probabilistic graphical model
rare event
tail dependence
Water discharge
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Summary: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.
ISSN:0303-6898
1467-9469
DOI:10.1111/sjos.12698