Estimating an extreme Bayesian network via scalings

Claudia Klüppelberg and Mario Krali

Journal of Multivariate Analysis, 2021, vol. 181, issue C

Abstract: A recursive max-linear vector models 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.

Keywords: Bayesian network; Causal order; Directed acyclic graph; Extreme value statistics; Graphical model; Recursive max-linear model; Regular variation; Structural equation model; Structure learning (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.jmva.2020.104672

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