Estimation of the coefficient of tail dependence in bivariate extremes
type: Item
instance of: scholarly article
title: Estimation of the coefficient of tail dependence in bivariate extremes
zbMATH Open document ID: 0958.62049
DOI: 10.1016/S0167-7152(98)00280-6
author: Yanyan Li
published in: Statistics \& Probability Letters
publication date: 2001-04-04T00:00:00Z
review text: Suppose a bivariate random vector \((X,Y)\) is in the domain of attraction of an extreme value distribution. Under certain assumptions on the bivariate upper tail behavior of \((X,Y)\), \textit{A.W. Ledford} and \textit{J.A. Tawn} [Biometrika 83, No. 1, 169-187 (1996; Zbl 0865.62040)] introduced an index of tail dependence \(\eta\) and studied the asymptotic properties of its estimator proposed by them. Here, under a more restrictive assumption on the bivariate tail behavior that makes \(\eta < 1\) if and only if the component random variables are asymptotically (upper-tail) independent, a nonparametric estimator is proposed and is shown to be asymptotically normal. It is used to estimate \(P(X > x, Y > y)\) for large \(x, y\). This estimator is also used to test asymptotic independence for a data on storm events.
Mathematics Subject Classification ID: 62G32
Mathematics Subject Classification ID: 62G20
zbMATH DE Number: 1395199
zbMATH Keywords: bivariate extremes
zbMATH Keywords: tail dependence
zbMATH Keywords: regular variation
zbMATH Keywords: nonparametric estimation
reviewed by: H. N. Nagaraja
MaRDI profile type: Publication
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Wikidata QID: Q127237906
description: scientific article; zbMATH DE number 1395199