The Annals of Statistics

An M-estimator for tail dependence in arbitrary dimensions

John H. J. Einmahl, Andrea Krajina, and Johan Segers

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Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as the value that minimizes the distance between a vector of weighted integrals of the tail dependence function and their empirical counterparts. The minimization problem has, with probability tending to one, a unique, global solution. The estimator is consistent and asymptotically normal. The spectral measures of the tail dependence models to which the method applies can be discrete or continuous. Examples demonstrate the applicability and the performance of the method.

Article information

Ann. Statist., Volume 40, Number 3 (2012), 1764-1793.

First available in Project Euclid: 2 October 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G32: Statistics of extreme values; tail inference 62G05: Estimation 62G10: Hypothesis testing 62G20: Asymptotic properties 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60F05: Central limit and other weak theorems 60F17: Functional limit theorems; invariance principles 60G70: Extreme value theory; extremal processes

Asymptotic statistics factor model M-estimation multivariate extremes tail dependence


Einmahl, John H. J.; Krajina, Andrea; Segers, Johan. An M-estimator for tail dependence in arbitrary dimensions. Ann. Statist. 40 (2012), no. 3, 1764--1793. doi:10.1214/12-AOS1023.

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