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An Extreme Value Bayesian Lasso for the Conditional Left and Right Tails

Author

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  • M. Carvalho

    (University of Edinburgh)

  • S. Pereira

    (Universidade de Lisboa)

  • P. Pereira

    (EST Setúbal/IPS and CEAUL)

  • P. Zea Bermudez

    (Universidade de Lisboa)

Abstract

We introduce a novel regression model for the conditional left and right tail of a possibly heavy-tailed response. The proposed model can be used to learn the effect of covariates on an extreme value setting via a Lasso-type specification based on a Lagrangian restriction. Our model can be used to track if some covariates are significant for the lower values, but not for the (right) tail—and vice versa; in addition to this, the proposed model bypasses the need for conditional threshold selection in an extreme value theory framework. We assess the finite-sample performance of the proposed methods through a simulation study that reveals that our method recovers the true conditional distribution over a variety of simulation scenarios, along with being accurate on variable selection. Rainfall data are used to showcase how the proposed method can learn to distinguish between key drivers of moderate rainfall, against those of extreme rainfall. Supplementary materials accompanying this paper appear online.

Suggested Citation

  • M. Carvalho & S. Pereira & P. Pereira & P. Zea Bermudez, 2022. "An Extreme Value Bayesian Lasso for the Conditional Left and Right Tails," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 222-239, June.
    • Handle: RePEc:spr:jagbes:v:27:y:2022:i:2:d:10.1007_s13253-021-00469-9
    DOI: 10.1007/s13253-021-00469-9
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    References listed on IDEAS

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    Cited by:

    1. Federica Stolf & Antonio Canale, 2023. "A hierarchical Bayesian non‐asymptotic extreme value model for spatial data," Environmetrics, John Wiley & Sons, Ltd., vol. 34(7), November.
    2. Philémon Gamet & Jonathan Jalbert, 2022. "A flexible extended generalized Pareto distribution for tail estimation," Environmetrics, John Wiley & Sons, Ltd., vol. 33(6), September.
    3. Julien Hambuckers & Marie Kratz & Antoine Usseglio-Carleve, 2023. "Efficient Estimation In Extreme Value Regression Models Of Hedge Fund Tail Risks," Working Papers hal-04090916, HAL.
    4. Julien Hambuckers & Marie Kratz & Antoine Usseglio-Carleve, 2023. "Efficient Estimation in Extreme Value Regression Models of Hedge Fund Tail Risks," Papers 2304.06950, arXiv.org.

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