Asymptotic behavior of an intrinsic rank-based estimator of the Pickands dependence function constructed from B-splines

Axel Bücher, Christian Genest*, Richard A. Lockhart, Johanna G. Nešlehová

*Corresponding author for this work

Publication: Scientific journalJournal articlepeer-review


A bivariate extreme-value copula is characterized by its Pickands dependence function, i.e., a convex function defined on the unit interval satisfying boundary conditions. This paper investigates the large-sample behavior of a nonparametric estimator of this function due to Cormier et al. (Extremes 17:633–659, 2014). These authors showed how to construct this estimator through constrained quadratic median B-spline smoothing of pairs of pseudo-observations derived from a random sample. Their estimator is shown here to exist whatever the order m≥ 3 of the B-spline basis, and its consistency is established under minimal conditions. The large-sample distribution of this estimator is also determined under the additional assumption that the underlying Pickands dependence function is a B-spline of given order with a known set of knots.

Original languageEnglish
Pages (from-to)101-138
Number of pages38
Issue number1
Publication statusPublished - Mar 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022, The Author(s).


  • 60G70
  • 62G32
  • 62H10
  • B-spline
  • Extreme-value copula
  • Minimum distance estimator
  • Pickands dependence function
  • Rank-based inference
  • Spectral distribution

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