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Name: Sebastian Engelke

Talk Title: Extremal Graphical Lasso and High-dimensional Extremes

Abstract: Statistical inference for the extremal graphical models introduced in Engelke and Hitz (2020, JRSSB) is so far restricted to simple structures called block graphs. We develop an extremal graphical lasso that can be used estimate in a data-driven way the structure in general H\"usler--Reiss graphical models. We propose an efficient algorithm and prove that it recovers the unerlying graph structure consistently even for growing dimension $d$. This enables the use of the extremal graphical lasso in high-dimensional settings where the sample size $n$ is comparable or larger than $d$. In extremes, such settings are of particular interest since the effective sample size, namely the number $k$ of exceedances, is much smaller than $n$.

This talk is an invited talk at EVA 2021.