Local robust estimation of the pickands dependence function

Mikael Escobar-Bach, Yuri Goegebeur, Armelle Guillou

Research output: Contribution to journalJournal articleResearchpeer-review

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.

Original languageEnglish
JournalAnnals of Statistics
Volume46
Issue number6A
Pages (from-to)2806-2843
ISSN0090-5364
DOIs
Publication statusPublished - 2018

Fingerprint

Dependence Function
Robust Estimation
Power Divergence
Estimator
Air Pollution
Gaussian Process
Asymptotic Properties
Covariates
Stochastic Processes
Simulation Study
Robust estimation
Framework
Stochastic processes
Divergence
Air pollution
Finite sample
Asymptotic properties
Simulation study
Gaussian process

Keywords

  • Conditional pickands dependence function
  • Robustness
  • Stochastic convergence

Cite this

Escobar-Bach, Mikael ; Goegebeur, Yuri ; Guillou, Armelle. / Local robust estimation of the pickands dependence function. In: Annals of Statistics. 2018 ; Vol. 46, No. 6A. pp. 2806-2843.
@article{4cc760672a7843cd9e03dc9af63b58bb,
title = "Local robust estimation of the pickands dependence function",
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.",
keywords = "Conditional pickands dependence function, Robustness, Stochastic convergence",
author = "Mikael Escobar-Bach and Yuri Goegebeur and Armelle Guillou",
year = "2018",
doi = "10.1214/17-AOS1640",
language = "English",
volume = "46",
pages = "2806--2843",
journal = "Annals of Statistics",
issn = "0090-5364",
publisher = "Institute of Mathematical Statistics",
number = "6A",

}

Local robust estimation of the pickands dependence function. / Escobar-Bach, Mikael; Goegebeur, Yuri; Guillou, Armelle.

In: Annals of Statistics, Vol. 46, No. 6A, 2018, p. 2806-2843.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Local robust estimation of the pickands dependence function

AU - Escobar-Bach, Mikael

AU - Goegebeur, Yuri

AU - Guillou, Armelle

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Conditional pickands dependence function

KW - Robustness

KW - Stochastic convergence

U2 - 10.1214/17-AOS1640

DO - 10.1214/17-AOS1640

M3 - Journal article

VL - 46

SP - 2806

EP - 2843

JO - Annals of Statistics

JF - Annals of Statistics

SN - 0090-5364

IS - 6A

ER -