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On the estimation of extreme directional multivariate quantiles

Author

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  • Raúl Torres
  • Elena Di Bernardino
  • Henry Laniado
  • Rosa E. Lillo

Abstract

In multivariate extreme value theory (MEVT), the focus is on analysis outside of the observable sampling zone, which implies that the region of interest is associated to high risk levels. This work provides tools to include directional notions into the MEVT, giving the opportunity to characterize the recently introduced directional multivariate quantiles (DMQ) at high levels. Then, an out-sample estimation method for these quantiles is given. A bootstrap procedure carries out the estimation of the tuning parameter in this multivariate framework and helps with the estimation of the DMQ. Asymptotic normality for the proposed estimator is provided and the methodology is illustrated with simulated data-sets. Finally, a real-life application to a financial case is also performed.

Suggested Citation

  • Raúl Torres & Elena Di Bernardino & Henry Laniado & Rosa E. Lillo, 2020. "On the estimation of extreme directional multivariate quantiles," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(22), pages 5504-5534, November.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:22:p:5504-5534
    DOI: 10.1080/03610926.2019.1619770
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    Cited by:

    1. Pere, Jaakko & Ilmonen, Pauliina & Viitasaari, Lauri, 2024. "On extreme quantile region estimation under heavy-tailed elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 202(C).

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