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Max-linear graphical models with heavy-tailed factors on trees of transitive tournaments

Author

Listed:
  • Asenova, Stefka

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Segers, Johan

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

Graphical models with heavy-tailed factors can be used to model extremal depen- dence or causality between extreme events. In a Bayesian network, variables are recur- sively defined in terms of their parents according to a directed acyclic graph (DAG). We focus on max-linear graphical models with respect to a special type of graphs, which we call a tree of transitive tournaments. The latter are block graphs combining in a tree-like structure a finite number of transitive tournaments, each of which is a DAG in which every two nodes are connected. We study the limit of the joint tails of the max-linear model conditionally on the event that a given variable exceeds a high threshold. Under a suitable condition, the limiting distribution involves the factorization into indepen- dent increments along the shortest trail between two variables, thereby imitating the behavior of a Markov random field. We are also interested in the identifiability of the model parameters in case some variables are latent and only a subvector is observed. It turns out that the parameters are identifiable under a criterion on the nodes carrying the latent variables which is easy and quick to check.

Suggested Citation

  • Asenova, Stefka & Segers, Johan, 2022. "Max-linear graphical models with heavy-tailed factors on trees of transitive tournaments," LIDAM Discussion Papers ISBA 2022031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2022031
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    References listed on IDEAS

    as
    1. Sebastian Engelke & Adrien S. Hitz, 2020. "Graphical models for extremes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(4), pages 871-932, September.
    2. Einmahl, J.H.J. & Krajina, A. & Segers, J., 2011. "An M-Estimator for Tail Dependence in Arbitrary Dimensions," Discussion Paper 2011-013, Tilburg University, Center for Economic Research.
    3. Hu, Shuang & Peng, Zuoxiang & Segers, Johan, 2022. "Modelling multivariate extreme value distributions via Markov trees," LIDAM Discussion Papers ISBA 2022021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Asenova, Stefka Kirilova & Mazo, Gildas & Segers, Johan, 2021. "Inference on extremal dependence in the domain of attraction of a structured Hüsler–Reiss distribution motivated by a Markov tree with latent variables," LIDAM Reprints ISBA 2021004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Gissibl, Nadine & Klüppelberg, Claudia & Otto, Moritz, 2018. "Tail dependence of recursive max-linear models with regularly varying noise variables," Econometrics and Statistics, Elsevier, vol. 6(C), pages 149-167.
    6. Klüppelberg, Claudia & Krali, Mario, 2021. "Estimating an extreme Bayesian network via scalings," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    7. Nadine Gissibl & Claudia Klüppelberg & Steffen Lauritzen, 2021. "Identifiability and estimation of recursive max‐linear models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 188-211, March.
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    Cited by:

    1. Natalia Markovich & Marijus Vaičiulis, 2023. "Extreme Value Statistics for Evolving Random Networks," Mathematics, MDPI, vol. 11(9), pages 1-35, May.

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