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On tail index estimation based on multivariate data

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  • A. Dematteo
  • S. Clémençon

Abstract

This article is devoted to the study of tail index estimation based on i.i.d. multivariate observations, drawn from a standard heavy-tailed distribution, that is, of which Pareto-like marginals share the same tail index. A multivariate central limit theorem for a random vector, whose components correspond to (possibly dependent) Hill estimators of the common tail index α , is established under mild conditions. We introduce the concept of (standard) heavy-tailed random vector of tail index α and show how this limit result can be used in order to build an estimator of α with small asymptotic mean squared error, through a proper convex linear combination of the coordinates. Beyond asymptotic results, simulation experiments illustrating the relevance of the approach promoted are also presented.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:gnstxx:v:28:y:2016:i:1:p:152-176
    DOI: 10.1080/10485252.2015.1124105
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    Cited by:

    1. Daouia, Abdelaati & Padoan, Simone A. & Stupfler, Gilles, 2022. "Optimal weighted pooling for inference about the tail index and extreme quantiles," TSE Working Papers 22-1322, Toulouse School of Economics (TSE), revised 07 Jun 2023.
    2. Chen, Feifei & Meintanis, Simos G. & Zhu, Lixing, 2019. "On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 125-144.
    3. Beirlant, J. & Buitendag, S. & del Barrio, E. & Hallin, M. & Kamper, F., 2020. "Center-outward quantiles and the measurement of multivariate risk," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 79-100.
    4. 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.

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