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- Title
Structure learning for extremal tree models.
- Authors
Engelke, Sebastian; Volgushev, Stanislav
- Abstract
Extremal graphical models are sparse statistical models for multivariate extreme events. The underlying graph encodes conditional independencies and enables a visual interpretation of the complex extremal dependence structure. For the important case of tree models, we develop a data‐driven methodology for learning the graphical structure. We show that sample versions of the extremal correlation and a new summary statistic, which we call the extremal variogram, can be used as weights for a minimum spanning tree to consistently recover the true underlying tree. Remarkably, this implies that extremal tree models can be learned in a completely non‐parametric fashion by using simple summary statistics and without the need to assume discrete distributions, existence of densities or parametric models for bivariate distributions.
- Subjects
DISTRIBUTION (Probability theory); SPANNING trees; EXTREME value theory; VARIOGRAMS; PARETO distribution; TREES
- Publication
Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2022, Vol 84, Issue 5, p2055
- ISSN
1369-7412
- Publication type
Article
- DOI
10.1111/rssb.12556