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arXiv · 2102.06197

Estimating a Directed Tree for Extremes

Ngoc Mai Tran·Johannes Buck·Claudia Klüppelberg
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Abstract

We propose a new method to estimate a root-directed spanning tree from extreme data. A prominent example is a river network, to be discovered from extreme flow measured at a set of stations. Our new algorithm utilizes qualitative aspects of a max-linear Bayesian network, which has been designed for modelling causality in extremes. The algorithm estimates bivariate scores and returns a root-directed spanning tree. It performs extremely well on benchmark data and new data. We prove that the new estimator is consistent under a max-linear Bayesian network model with noise. We also assess its strengths and limitations in a small simulation study.

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BibTeXRIS

Ngoc Mai Tran, Johannes Buck, Claudia Klüppelberg. 2021-02-11. Estimating a Directed Tree for Extremes. https://arxiv.org/abs/2102.06197

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