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Characterization of valid auxiliary functions for representations of extreme value distributions and their max‐domains of attraction

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  • Miriam Isabel Seifert

Abstract

In this paper we study two important representations for extreme value distributions and their max‐domains of attraction (MDA), namely von Mises representation (vMR) and variation representation (VR), which are convenient ways to gain limit results. Both VR and vMR are defined via so‐called auxiliary functions ψ. Up to now, however, the set of valid auxiliary functions for vMR has neither been characterized completely nor separated from those for VR. We contribute to the current literature by introducing “universal” auxiliary functions which are valid for both VR and vMR representations for the entire MDA distribution families. Then we identify exactly the sets of valid auxiliary functions for both VR and vMR. Moreover, we propose a method for finding appropriate auxiliary functions with analytically simple structure and provide them for several important distributions.

Suggested Citation

  • Miriam Isabel Seifert, 2024. "Characterization of valid auxiliary functions for representations of extreme value distributions and their max‐domains of attraction," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(2), pages 832-860, June.
    • Handle: RePEc:bla:scjsta:v:51:y:2024:i:2:p:832-860
    DOI: 10.1111/sjos.12701
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    References listed on IDEAS

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    1. Claudia Klüppelberg & Miriam Isabel Seifert, 2019. "Financial risk measures for a network of individual agents holding portfolios of light-tailed objects," Finance and Stochastics, Springer, vol. 23(4), pages 795-826, October.
    2. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496, December.
    3. Vasyl Golosnoy & Iryna Okhrin & Wolfgang Schmid, 2012. "Statistical Surveillance of Volatility Forecasting Models," Journal of Financial Econometrics, Oxford University Press, vol. 10(3), pages 513-543, June.
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