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Identifiability and estimation of recursive max‐linear models

Author

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  • Nadine Gissibl
  • Claudia Klüppelberg
  • Steffen Lauritzen

Abstract

We address the identifiability and estimation of recursive max‐linear structural equation models represented by an edge‐weighted directed acyclic graph (DAG). Such models are generally unidentifiable and we identify the whole class of DAG s and edge weights corresponding to a given observational distribution. For estimation, standard likelihood theory cannot be applied because the corresponding families of distributions are not dominated. Given the underlying DAG, we present an estimator for the class of edge weights and show that it can be considered a generalized maximum likelihood estimator. In addition, we develop a simple method for identifying the structure of the DAG. With probability tending to one at an exponential rate with the number of observations, this method correctly identifies the class of DAGs and, similarly, exactly identifies the possible edge weights.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:48:y:2021:i:1:p:188-211
    DOI: 10.1111/sjos.12446
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    References listed on IDEAS

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    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, John & Kiriliouk, Anna & Segers, Johan, 2016. "A continuous updating weighted least squares estimator of tail dependence in high dimensions," LIDAM Discussion Papers ISBA 2016002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    Cited by:

    1. 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).
    2. Klüppelberg, Claudia & Sönmez, Ercan, 2022. "Max-linear models in random environment," Journal of Multivariate Analysis, Elsevier, vol. 190(C).

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