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 ℓ, and the Archimedean generator ψ which distorts the extreme-value dependence structure. This article develops semiparametric inference for Archimax copulas: a nonparametric estimator of ℓ and a moment-based estimator of ψ assuming the latter belongs to a parametric family. Conditions under which ψ and ℓ 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 ℓ reveals asymmetric extremal dependence between the stations, which reflects heavy precipitation patterns in the area. Technical proofs, simulation results and R code are provided in the Online Supplement.
|Seiten (von - bis)||1025-1051|
|Fachzeitschrift||Annals of Statistics|
|Publikationsstatus||Veröffentlicht - 2020|
Bibliographische NotizFunding Information:
This work was supported in part by the LABEX MILYON (ANR-10-LABX-0070) of Uni-versité de Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French Agence nationale de la recherche (ANR), and grants from the Natural Sciences and Engineering Research Council of Canada (RGPIN-2015-06801), the Fonds de recherche du Québec—Nature et technologies (2015–PR–183236) and the Canadian Statistical Sciences Institute.
© Institute of Mathematical Statistics, 2020