The Annals of Statistics

Local robust estimation of the Pickands dependence function

Mikael Escobar-Bach, Yuri Goegebeur, and Armelle Guillou

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aos/1536307234

Digital Object Identifier
doi:10.1214/17-AOS1640

Mathematical Reviews number (MathSciNet)
MR3851756

Zentralblatt MATH identifier
06968600

Subjects
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

Keywords
Conditional Pickands dependence function robustness stochastic convergence

Citation

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. https://projecteuclid.org/euclid.aos/1536307234


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