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November 2018 Max-linear models on directed acyclic graphs
Nadine Gissibl, Claudia Klüppelberg
Bernoulli 24(4A): 2693-2720 (November 2018). DOI: 10.3150/17-BEJ941


We consider a new recursive structural equation model where all variables can be written as max-linear function of their parental node variables and independent noise variables. The model is max-linear in terms of the noise variables, and its causal structure is represented by a directed acyclic graph. We detail the relation between the weights of the recursive structural equation model and the coefficients in its max-linear representation. In particular, we characterize all max-linear models which are generated by a recursive structural equation model, and show that its max-linear coefficient matrix is the solution of a fixed point equation. We also find the minimum directed acyclic graph representing the recursive structural equations of the variables. The model structure introduces a natural order between the node variables and the max-linear coefficients. This yields representations of the vector components, which are based on the minimum number of node and noise variables.


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Nadine Gissibl. Claudia Klüppelberg. "Max-linear models on directed acyclic graphs." Bernoulli 24 (4A) 2693 - 2720, November 2018.


Received: 1 January 2016; Revised: 1 February 2017; Published: November 2018
First available in Project Euclid: 26 March 2018

zbMATH: 06853262
MathSciNet: MR3779699
Digital Object Identifier: 10.3150/17-BEJ941

Keywords: Directed acyclic graph , Graphical model , max-linear model , minimal representation , path analysis , structural equation model

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability


Vol.24 • No. 4A • November 2018
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