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Trends in Extreme Value Indices

Author

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  • Laurens de Haan
  • Chen Zhou

Abstract

We consider extreme value analysis for independent but nonidentically distributed observations. In particular, the observations do not share the same extreme value index. Assuming continuously changing extreme value indices, we provide a nonparametric estimate for the functional extreme value index. Besides estimating the extreme value index locally, we also provide a global estimator for the trend and its joint asymptotic theory. The asymptotic theory for the global estimator can be used for testing a prespecified parametric trend in the extreme value indices. In particular, it can be applied to test whether the extreme value index remains at a constant level across all observations.

Suggested Citation

  • Laurens de Haan & Chen Zhou, 2021. "Trends in Extreme Value Indices," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(535), pages 1265-1279, July.
    • Handle: RePEc:taf:jnlasa:v:116:y:2021:i:535:p:1265-1279
    DOI: 10.1080/01621459.2019.1705307
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    Cited by:

    1. Einmahl, John & He, Y., 2022. "Extreme Value Inference for General Heterogeneous Data," Discussion Paper 2022-017, Tilburg University, Center for Economic Research.
    2. Einmahl, John & He, Y., 2022. "Extreme Value Inference for General Heterogeneous Data," Other publications TiSEM fd8dd91c-086f-40e6-ac29-3, Tilburg University, School of Economics and Management.
    3. Di Bernardino, Elena & Laloë, Thomas & Pakzad, Cambyse, 2024. "Estimation of extreme multivariate expectiles with functional covariates," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    4. Enzo D'Innocenzo & Andre Lucas & Bernd Schwaab & Xin Zhang, 2024. "Joint extreme Value-at-Risk and Expected Shortfall dynamics with a single integrated tail shape parameter," Tinbergen Institute Discussion Papers 24-069/III, Tinbergen Institute.
    5. Natalia Markovich & Marijus Vaičiulis, 2023. "Extreme Value Statistics for Evolving Random Networks," Mathematics, MDPI, vol. 11(9), pages 1-35, May.
    6. He, Yi & Einmahl, John, 2024. "Extreme Value Inference for General Heterogeneous Data," Other publications TiSEM 5d01cb7e-d528-406d-8c24-c, Tilburg University, School of Economics and Management.

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