Bivariate tail estimation: dependence in asymptotic independence
Gerrit Draisma, Holger Drees, Ana Ferreira, and Laurens De Haan
Source: Bernoulli Volume 10, Number 2
(2004), 251-280.
Abstract
In the classical setting of bivariate extreme value theory, the procedures for estimating the probability of an extreme event are not applicable if the componentwise maxima of the observations are asymptotically independent. To cope with this problem, Ledford and Tawn proposed a submodel in which the penultimate dependence is characterized by an additional parameter. We discuss the asymptotic properties of two estimators for this parameter in an extended model. Moreover, we develop an estimator for the probability of an extreme event that works in the case of asymptotic independence as well as in the case of asymptotic dependence, and prove its consistency.
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Keywords: asymptotic normality; bivariate extreme value distribution; coefficient of tail dependence; copula; failure probability; Hill estimator; moment estimator
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.bj/1082380219
Mathematical Reviews number (MathSciNet): MR2046774
Zentralblatt MATH identifier: 1058.62043
Digital Object Identifier: doi:10.3150/bj/1082380219
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