Local robust estimation of the Pickands dependence function
type: Item
instance of: scholarly article
title: Local robust estimation of the Pickands dependence function
zbMATH Open document ID: 1408.62095
DOI: 10.1214/17-AOS1640
author: Mikael Escobar-Bach
author: Yuri Goegebeur
author: Armelle Guillou
published in: The Annals of Statistics
publication date: 2018-10-30T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.aos/1536307234
review text: Let \(\left( Y^{(1)},Y^{(2)} \right) \) be a pair of random variables which is recorded along with a random covariate \( X \in \mathbb{R}^{p} \). Denote by \( C_{x}, F_{1}\left(\cdot | x \right) \) and \( F_{2}\left(\cdot | x \right) \) the conditional copula function and the continuous distribution functions of \( Y^{1} \) and \( Y^{2} \) given \( X=x \). The authors consider the model which is written as \[ \mathbb{P}\left(F_{1} \left( Y^{1} | x \right) \leq y_{1}, \quad F_{2} \left( Y^{2} | x \right) \leq y_{2} \right) = C_{x}\left( y_{1}, y_{2} \right), \] where the conditional extreme value copula \( C_{x} \) admits a representation of the form \[ C_{x}\left( y_{1},y_{2} \right) = \exp \left( \log\left( y_{1}y_{2} \right) A\left( \frac{\log\left( y_{2} \right)}{\log\left( y_{1}y_{2} \right)} \Big| x \right) \right), \] and \( A\left(\cdot|\cdot \right) : [0,1] \times \mathbb{R}^{p} \to [1/2,1]\) is the conditional Pickands dependence function. The authors' 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.
reviewed by: Wiesław Dziubdziela
Mathematics Subject Classification ID: 62G32
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 62P12
zbMATH DE Number: 6968600
zbMATH Keywords: conditional Pickands dependence function
zbMATH Keywords: robustness
zbMATH Keywords: stochastic convergence
MaRDI profile type: Publication
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OpenAlex ID: W2460442175
description: scientific article; zbMATH DE number 6968600