Open Access
April 2020 Inference for Archimax copulas
Simon Chatelain, Anne-Laure Fougères, Johanna G. Nešlehová
Ann. Statist. 48(2): 1025-1051 (April 2020). DOI: 10.1214/19-AOS1836


Archimax copula models can account for any type of asymptotic dependence between extremes and at the same time capture joint risks at medium levels. An Archimax copula is characterized by two functional parameters: the stable tail dependence function $\ell $, and the Archimedean generator $\psi $ which distorts the extreme-value dependence structure. This article develops semiparametric inference for Archimax copulas: a nonparametric estimator of $\ell $ and a moment-based estimator of $\psi $ assuming the latter belongs to a parametric family. Conditions under which $\psi $ and $\ell $ are identifiable are derived. The asymptotic behavior of the estimators is then established under broad regularity conditions; performance in small samples is assessed through a comprehensive simulation study. The Archimax copula model with the Clayton generator is then used to analyze monthly rainfall maxima at three stations in French Brittany. The model is seen to fit the data very well, both in the lower and in the upper tail. The nonparametric estimator of $\ell $ reveals asymmetric extremal dependence between the stations, which reflects heavy precipitation patterns in the area. Technical proofs, simulation results and $\mathsf{R}$ code are provided in the Online Supplement.


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Simon Chatelain. Anne-Laure Fougères. Johanna G. Nešlehová. "Inference for Archimax copulas." Ann. Statist. 48 (2) 1025 - 1051, April 2020.


Received: 1 June 2018; Revised: 1 February 2019; Published: April 2020
First available in Project Euclid: 26 May 2020

zbMATH: 07241579
MathSciNet: MR4102686
Digital Object Identifier: 10.1214/19-AOS1836

Primary: 62G05 , 62G20 , 62G32 , 62H12
Secondary: 60G70

Keywords: copulas , Empirical processes , multivariate extremes , subasymptotic modeling

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 2 • April 2020
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