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Exploiting occurrence times in likelihood inference for componentwise maxima

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  • Alec Stephenson
  • Jonathan Tawn

Abstract

Multivariate extreme value distributions arise as the limiting distributions of normalised componentwise maxima. They are often used to model multivariate data that can be regarded as the componentwise maxima of some unobserved underlying multivariate process. In many applications we have extra information. We often know the locations of the maxima within the underlying process. If the process is temporal this knowledge is frequently available through the dates on which the maxima are recorded. We show how to incorporate this extra information into maximum likelihood procedures. Asymptotic and small-sample efficiency results are presented for the dependence parameter in the logistic parametric sub-class of bivariate extreme value distributions. We conclude with an application to sea levels. Copyright 2005, Oxford University Press.

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  • Alec Stephenson & Jonathan Tawn, 2005. "Exploiting occurrence times in likelihood inference for componentwise maxima," Biometrika, Biometrika Trust, vol. 92(1), pages 213-227, March.
    • Handle: RePEc:oup:biomet:v:92:y:2005:i:1:p:213-227
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    File URL: http://hdl.handle.net/10.1093/biomet/92.1.213
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    Citations

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    Cited by:

    1. R de Fondeville & A C Davison, 2018. "High-dimensional peaks-over-threshold inference," Biometrika, Biometrika Trust, vol. 105(3), pages 575-592.
    2. Alexis Bienvenüe & Christian Y. Robert, 2017. "Likelihood Inference for Multivariate Extreme Value Distributions Whose Spectral Vectors have known Conditional Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 130-149, March.
    3. Raphaël Huser & Thomas Opitz & Emeric Thibaud, 2021. "Max‐infinitely divisible models and inference for spatial extremes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 321-348, March.
    4. Stoev, Stilian & Wang, Yizao, 2019. "Exchangeable random partitions from max-infinitely-divisible distributions," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 50-56.
    5. Vettori, Sabrina & Huser, Raphael & Segers, Johan & Genton, Marc, 2017. "Bayesian Clustering and Dimension Reduction in Multivariate Extremes," LIDAM Discussion Papers ISBA 2017017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Carsten Bormann & Melanie Schienle, 2020. "Detecting Structural Differences in Tail Dependence of Financial Time Series," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 380-392, April.
    7. Raphaël Huser & Marc G. Genton, 2016. "Non-Stationary Dependence Structures for Spatial Extremes," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 470-491, September.
    8. Lee, Xing Ju & Hainy, Markus & McKeone, James P. & Drovandi, Christopher C. & Pettitt, Anthony N., 2018. "ABC model selection for spatial extremes models applied to South Australian maximum temperature data," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 128-144.

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