INFERENCE FOR ARCHIMAX COPULAS

• 成果类型: Article
• 署名作者: Chatelain, Simon; Fougeres, Anne-Laure; Neslehova, Johanna G.
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; CNRS - National Institute for Mathematical Sciences (INSMI); McGill University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1836
• 发表日期: 2020
• 页码: 1025-1051
• 关键词: nonparametric-estimation; dependence-function; tail dependence; extreme; distributions; INDEPENDENCE

摘要

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 psi 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 psi assuming the latter belongs to a parametric family. Conditions under which psi 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 rainfallmaxima 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.