|
Abstract:
|
Multivariate extreme value theory is interested in the dependence structure of multivariate data in the unobserved far tail regions. Multiple characterizations and models exist for such extremal dependence structure. However, statistical inference for those extremal dependence models uses merely a fraction of the available data, which drastically reduces the effective sample size, creating challenges even in moderate dimension. Engelke & Hitz (2020, JRSSB) introduced graphical modelling for multivariate extremes, allowing for enforced sparsity in moderate- to high-dimensional settings. Yet, the model selection and estimation tools that appear therein are limited to simple graph structures. In this work, we propose a novel, scalable method for selection and estimation of extremal graphical models that makes no assumption on the underlying graph structure. It is based on existing tools for Gaussian graphical model selection such as the graphical lasso and the neighborhood selection approach. Model selection consistency is established in sparse regimes where the dimension is allowed to be exponentially larger than the effective sample size.
|
