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Estimating an extreme Bayesian network via scalings. (English) Zbl 1461.62083

Summary: 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.

MSC:

62H22 Probabilistic graphical models
62R01 Algebraic statistics
62G30 Order statistics; empirical distribution functions
62G32 Statistics of extreme values; tail inference
60G70 Extreme value theory; extremal stochastic processes
60F10 Large deviations
65S05 Graphical methods in numerical analysis
05C90 Applications of graph theory
62P10 Applications of statistics to biology and medical sciences; meta analysis
62P05 Applications of statistics to actuarial sciences and financial mathematics

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References:

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