On second order conditions in the multivariate block maxima and peak over threshold method

Axel Bücher*, Stanislav Volgushev, Nan Zou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Second order conditions provide a natural framework for establishing asymptotic results about estimators for tail related quantities. Such conditions are typically tailored to the estimation principle at hand, and may be vastly different for estimators based on the block maxima (BM) method or the peak-over-threshold (POT) approach. In this paper we provide details on the relationship between typical second order conditions for BM and POT methods in the multivariate case. We show that the two conditions typically imply each other, but with a possibly different second order parameter. The latter implies that, depending on the data generating process, one of the two methods can attain faster convergence rates than the other. The class of multivariate Archimax copulas is examined in detail; we find that this class contains models for which the second order parameter is smaller for the BM method and vice versa. The theory is illustrated by a small simulation study.
Original languageEnglish
Pages (from-to)604-619
Number of pages16
JournalJournal of Multivariate Analysis
Publication statusPublished - Sept 2019
Externally publishedYes


  • Archimax copulas
  • Domain of attraction
  • Extremal dependence
  • Extreme value statistics
  • Pickands dependence function
  • Madogram


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