IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v48y2021i1p188-211.html
   My bibliography  Save this article

Identifiability and estimation of recursive max‐linear models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/sjos.12446
    Download Restriction: no
    File URL: https://libkey.io/10.1111/sjos.12446?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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, 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).
    3. Einmahl, John & Kiriliouk, A. & Segers, J.J.J., 2016. "A Continuous Updating Weighted Least Squares Estimator of Tail Dependence in High Dimensions," Discussion Paper 2016-002, Tilburg University, Center for Economic Research.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hentschel, Manuel & Engelke, Sebastian & Segers, Johan, 2022. "Statistical Inference for Hüsler–Reiss Graphical Models Through Matrix Completions," LIDAM Discussion Papers ISBA 2022032, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Klüppelberg, Claudia & Krali, Mario, 2021. "Estimating an extreme Bayesian network via scalings," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    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. 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.
    5. Einmahl, John & Segers, Johan, 2020. "Empirical Tail Copulas for Functional Data," Discussion Paper 2020-004, Tilburg University, Center for Economic Research.
    6. Kiriliouk, Anna, 2020. "Hypothesis testing for tail dependence parameters on the boundary of the parameter space," Econometrics and Statistics, Elsevier, vol. 16(C), pages 121-135.
    7. Asenova, Stefka Kirilova & Mazo, Gildas & Segers, Johan, 2020. "Inference on extremal dependence in a latent Markov tree model attracted to a Husler-Reiss distribution," LIDAM Discussion Papers ISBA 2020005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Miranda J. Fix & Daniel S. Cooley & Emeric Thibaud, 2021. "Simultaneous autoregressive models for spatial extremes," Environmetrics, John Wiley & Sons, Ltd., vol. 32(2), March.
    9. Kiriliouk, Anna & Lee, Jeongjin & Segers, Johan, 2023. "X-Vine Models for Multivariate Extremes," LIDAM Discussion Papers ISBA 2023038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Samuel A. Morris & Brian J. Reich & Emeric Thibaud, 2019. "Exploration and Inference in Spatial Extremes Using Empirical Basis Functions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(4), pages 555-572, December.
    11. Segers, Johan, 2019. "One- versus multi-component regular variation and extremes of Markov trees," LIDAM Discussion Papers ISBA 2019001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Einmahl, John & Segers, Johan, 2020. "Empirical Tail Copulas for Functional Data," Discussion Paper 2020-004, Tilburg University, Center for Economic Research.
    13. Sebastian Engelke & Stanislav Volgushev, 2022. "Structure learning for extremal tree models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 2055-2087, November.
    14. Junshu Jiang & Jordan Richards & Raphael Huser & David Bolin, 2024. "The Efficient Tail Hypothesis: An Extreme Value Perspective on Market Efficiency," Papers 2408.06661, arXiv.org.
    15. Asenova, Stefka & Segers, Johan, 2022. "Extremes of Markov random fields on block graphs," LIDAM Discussion Papers ISBA 2022013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    16. Christis Katsouris, 2023. "Statistical Estimation for Covariance Structures with Tail Estimates using Nodewise Quantile Predictive Regression Models," Papers 2305.11282, arXiv.org, revised Jul 2023.
    17. 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).
    18. Christis Katsouris, 2023. "High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods," Papers 2308.16192, arXiv.org.
    19. Juraj Bodik, 2024. "Extreme Treatment Effect: Extrapolating Dose-Response Function into Extreme Treatment Domain," Mathematics, MDPI, vol. 12(10), pages 1-36, May.
    20. Mourahib, Anas & Kiriliouk, Anna & Segers, Johan, 2023. "Multivariate generalized Pareto distributions along extreme directions," LIDAM Discussion Papers ISBA 2023034, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:scjsta:v:48:y:2021:i:1:p:188-211. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.