Affiliation:
1. School of Science/Key Laboratory of Intelligent Analysis and Decision on Complex Systems Chongqing University of Posts and Telecommunications Chongqing China
2. LIDAM/ISBA Universite Catholique de Louvain Louvain la Neuve Belgium
3. School of Mathematics and Statistics Southwest University Chongqing China
Abstract
AbstractMultivariate 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.
Funder
China Scholarship Council
Subject
Statistics, Probability and Uncertainty,Statistics and Probability
Cited by
1 articles.
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