The Annals of Statistics

Local robust estimation of the Pickands dependence function

Mikael Escobar-Bach, Yuri Goegebeur, and Armelle Guillou

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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.

Article information

Ann. Statist., Volume 46, Number 6A (2018), 2806-2843.

Received: June 2016
Revised: May 2017
First available in Project Euclid: 7 September 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G32: Statistics of extreme values; tail inference 62G05: Estimation 62G20: Asymptotic properties
Secondary: 60F05: Central limit and other weak theorems 60G70: Extreme value theory; extremal processes

Conditional Pickands dependence function robustness stochastic convergence


Escobar-Bach, Mikael; Goegebeur, Yuri; Guillou, Armelle. Local robust estimation of the Pickands dependence function. Ann. Statist. 46 (2018), no. 6A, 2806--2843. doi:10.1214/17-AOS1640.

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