LOCAL ROBUST ESTIMATION OF THE PICKANDS DEPENDENCE FUNCTION

• 成果类型: Article
• 署名作者: Escobar-Bach, Mikael; Goegebeur, Yuri; Guillou, Armelle
• 署名单位: University of Southern Denmark; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1640
• 发表日期: 2018
• 页码: 2806-2843
• 关键词: uniform consistency; rates

摘要

We consider the robust estimation of the Pickands dependence function in the random covariate framework. Our estimator is based on local estimation with the minimum density power divergence criterion. We provide the main asymptotic properties, in particular the convergence of the stochastic process, correctly normalized, towards a tight centered Gaussian process. The finite sample performance of our estimator is evaluated with a simulation study involving both uncontaminated and contaminated samples. The method is illustrated on a dataset of air pollution measurements.