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Regression models for exceedance data: a new approach

Author

Listed:
  • Marcelo Bourguignon

    (Universidade Federal do Rio Grande do Norte)

  • Fernando Ferraz Nascimento

    (Universidade Federal do Piauí)

Abstract

The generalized Pareto distribution (GPD) is a family of continuous distributions used to model the tail of the distribution to values higher than a threshold u. Despite the advantages of the GPD representation, its shape and scale parameters do not correspond to the expected value, which complicates the interpretation of regression models specified using the GPD. This study proposes a linear regression model in which the response variable is a GPD, using a new parametrization that is indexed by mean and precision parameters. The main advantage of our new parametrization is the straightforward interpretation of the regression coefficients in terms of the expectation of the positive real line response variable, as is usual in the context of generalized linear models. Furthermore, we propose a model for extreme values, in which the GPD parameters (mean and precision) are defined on the basis of a dynamic linear regression model. The novelty of the study lies in the time variation of the mean and precision parameter of the resulting distribution. The parameter estimation of these new models is performed under the Bayesian paradigm. Simulations are conducted to analyze the performance of our proposed models. Finally, the models are applied to environmental datasets (temperature datasets), illustrating their capabilities in challenging cases in extreme value theory.

Suggested Citation

  • Marcelo Bourguignon & Fernando Ferraz Nascimento, 2021. "Regression models for exceedance data: a new approach," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 157-173, March.
    • Handle: RePEc:spr:stmapp:v:30:y:2021:i:1:d:10.1007_s10260-020-00518-6
    DOI: 10.1007/s10260-020-00518-6
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    References listed on IDEAS

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    1. Fernando Nascimento & Dani Gamerman & Hedibert Lopes, 2016. "Time-varying extreme pattern with dynamic models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 131-149, March.
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    Cited by:

    1. Marcelo Bourguignon & Diego I. Gallardo & Héctor J. Gómez, 2022. "A Note on Pareto-Type Distributions Parameterized by Its Mean and Precision Parameters," Mathematics, MDPI, vol. 10(3), pages 1-8, February.

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