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2021 Recursive max-linear models with propagating noise
Johannes Buck, Claudia Klüppelberg
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Electron. J. Statist. 15(2): 4770-4822 (2021). DOI: 10.1214/21-EJS1903


Recursive max-linear vectors model causal dependence between node variables by a structural equation model, expressing each node variable as a max-linear function of its parental nodes in a directed acyclic graph (DAG) and some exogenous innovation. For such a model, there exists a unique minimum DAG, represented by the Kleene star matrix of its edge weight matrix, which identifies the model and can be estimated. For a more realistic statistical modeling we introduce some random observational noise. A probabilistic analysis of this new noisy model reveals that the unique minimum DAG representing the distribution of the non-noisy model remains unchanged and identifiable. Moreover, the distribution of the minimum ratio estimators of the model parameters at their left limits are completely determined by the distribution of the noise variables up to a positive constant. Under a regular variation condition on the noise variables we prove that the estimated Kleene star matrix converges to a matrix of independent Weibull entries after proper centering and scaling.


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Johannes Buck. Claudia Klüppelberg. "Recursive max-linear models with propagating noise." Electron. J. Statist. 15 (2) 4770 - 4822, 2021.


Received: 1 May 2020; Published: 2021
First available in Project Euclid: 30 September 2021

Digital Object Identifier: 10.1214/21-EJS1903

Primary: 60G70 , 62F12 , 62G32 , 62H22

Keywords: Bayesian network , Directed acyclic graph , Extreme value analysis , Graphical model , max-linear model , noisy model , regular variation


Vol.15 • No. 2 • 2021
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