Graphical lasso for extremes

TL;DR

This paper introduces a method to estimate sparse dependence structures in the tails of high-dimensional multivariate data using a graphical model for extremes, with proven consistency and demonstrated effectiveness.

Contribution

It proposes the extreme graphical lasso, a novel technique for modeling tail dependence with sparsity, extending graphical models to extreme value analysis.

Findings

The method accurately identifies the graph structure in simulations.

The approach is effective on real data examples.

Theoretical proof of consistency is provided.

Abstract

In this paper, we estimate the sparse dependence structure in the tail region of a multivariate random vector, potentially of high dimension. The tail dependence is modeled via a graphical model for extremes embedded in the H\"usler-Reiss distribution. We propose the extreme graphical lasso procedure to estimate the sparsity in the tail dependence, similar to the Gaussian graphical lasso in high dimensional statistics. We prove its consistency in identifying the graph structure and estimating model parameters. The efficiency and accuracy of the proposed method are illustrated by simulations and real data examples.