Estimating an Extreme Bayesian Network via Scalings

TL;DR

This paper introduces a new scaling method for estimating causal structures in extreme Bayesian networks with regularly varying innovations, providing asymptotic properties and applying it to financial and dietary data.

Contribution

It proposes a novel scaling technique for causal order estimation in extreme Bayesian networks with regular variation, including asymptotic analysis and practical applications.

Findings

Successful estimation of causal order using scalings

Asymptotic normality of estimators established

Application to real-world financial and dietary data

Abstract

Recursive max-linear vectors model causal dependence between its components by expressing each node variable as a max-linear function of its parental nodes in a directed acyclic graph and some exogenous innovation. Motivated by extreme value theory, innovations are assumed to have regularly varying distribution tails. We propose a scaling technique in order to determine a causal order of the node variables. All dependence parameters are then estimated from the estimated scalings. Furthermore, we prove asymptotic normality of the estimated scalings and dependence parameters based on asymptotic normality of the empirical spectral measure. Finally, we apply our structure learning and estimation algorithm to financial data and food dietary interview data.