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Estimation of the tail exponent of multivariate regular variation

Author

Listed:
  • Moosup Kim

    (APEC Climate Center)

  • Sangyeol Lee

    (Seoul National University)

Abstract

In this study, we consider the problem of estimating the tail exponent of multivariate regular variation. Since any convex combination of a random vector with a multivariate regularly varying tail has a univariate regularly varying tail with the same exponent under certain conditions, to estimate the tail exponent of the multivariate regular variation of a given random vector, we employ a weighted average of Hill’s estimators obtained for all of its convex combinations, designed to reduce the variability of estimation. We investigate the asymptotic properties and evaluate the finite sample performance of the weighted average of Hill’s estimators. A simulation study and real data analysis are provided for illustration.

Suggested Citation

  • Moosup Kim & Sangyeol Lee, 2017. "Estimation of the tail exponent of multivariate regular variation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 945-968, October.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:5:d:10.1007_s10463-016-0574-9
    DOI: 10.1007/s10463-016-0574-9
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    References listed on IDEAS

    as
    1. A. Dematteo & S. Clémençon, 2016. "On tail index estimation based on multivariate data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 152-176, March.
    2. Georg Mainik & Ludger Rüschendorf, 2010. "On optimal portfolio diversification with respect to extreme risks," Finance and Stochastics, Springer, vol. 14(4), pages 593-623, December.
    3. M. Ivette Gomes & Laurens De Haan & Lígia Henriques Rodrigues, 2008. "Tail index estimation for heavy‐tailed models: accommodation of bias in weighted log‐excesses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 31-52, February.
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