B1087
Title: Heavy-tailed max-linear structural equation models in networks with hidden nodes
Authors: Mario Krali - EPFL (Switzerland) [presenting]
Anthony Davison - EPFL (Switzerland)
Claudia Klueppelberg - Technische Universitaet Muenchen (Germany)
Abstract: Recursive max-linear vectors provide models for the causal dependence between large values of observed random variables as they are supported on directed acyclic graphs (DAGs). However, the standard assumption that all nodes of such a DAG are observed is often unrealistic. Necessary and sufficient conditions are provided that allow for a partially observed vector from a regularly varying model to be represented as a recursive max-linear (sub-)model. The method relies on regular variation and the minimal representation of a recursive max-linear vector. The max-weighted paths of a DAG play an essential role. Results are based on a scaling technique and causal dependence relations between pairs of nodes. In certain cases, the method can also detect the presence of hidden confounders. Under a two-step thresholding procedure, consistency and asymptotic normality of the estimators are shown. Finally, the method is studied by simulation, and nutrition intake data is applied it to.
