Open Access
June 2012 An M-estimator for tail dependence in arbitrary dimensions
John H. J. Einmahl, Andrea Krajina, Johan Segers
Ann. Statist. 40(3): 1764-1793 (June 2012). DOI: 10.1214/12-AOS1023


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.


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John H. J. Einmahl. Andrea Krajina. Johan Segers. "An M-estimator for tail dependence in arbitrary dimensions." Ann. Statist. 40 (3) 1764 - 1793, June 2012.


Published: June 2012
First available in Project Euclid: 2 October 2012

zbMATH: 1257.62058
MathSciNet: MR3015043
Digital Object Identifier: 10.1214/12-AOS1023

Primary: 60K35 , 62G05 , 62G10 , 62G20 , 62G32
Secondary: 60F05 , 60F17 , 60G70

Keywords: Asymptotic statistics , factor model , M-estimation , multivariate extremes , tail dependence

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 3 • June 2012
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