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

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...

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Bibliographic Details
Published in:Extremes (Boston) 2023-03, Vol.26 (1), p.101-138
Main Authors: Bücher, Axel, Genest, Christian, Lockhart, Richard A., Nešlehová, Johanna G.
Format: Article
Language:English
Subjects:
Asymptotic properties
Bivariate analysis
Boundary conditions
Civil Engineering
Economics
Environmental Management
Extreme values
Finance
Hydrogeology
Insurance
Management
Mathematics and Statistics
Quality Control
Reliability
Safety and Risk
Spline functions
Statistics
Statistics for Business
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Summary: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.
ISSN:1386-1999
1572-915X
DOI:10.1007/s10687-022-00451-9