An M-Estimator for Tail Dependence in Arbitrary Dimensions

J.H.J. Einmahl, A. Krajina, J. Segers

Research output: Working paperDiscussion paperOther research output

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Abstract

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 minimises the distance between a vector of weighted integrals of the tail dependence function and their empirical counterparts. The minimisation 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.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Volume2011-013
Publication statusPublished - 2011

Publication series

NameCentER Discussion Paper
Volume2011-013

Fingerprint

Tail Dependence
M-estimator
Multivariate Extreme Value Distribution
Dependence Function
Estimator
Spectral Measure
Domain of Attraction
Dependence Structure
Arbitrary
Parametric Model
Global Solution
Unknown Parameters
Minimization Problem
Attractor
Minimise
Demonstrate
Model

Keywords

  • asymptotic statistics
  • factor model
  • M-estimation
  • multivariate extremes
  • tail dependence

Cite this

Einmahl, J. H. J., Krajina, A., & Segers, J. (2011). An M-Estimator for Tail Dependence in Arbitrary Dimensions. (CentER Discussion Paper; Vol. 2011-013). Tilburg: Econometrics.
Einmahl, J.H.J. ; Krajina, A. ; Segers, J. / An M-Estimator for Tail Dependence in Arbitrary Dimensions. Tilburg : Econometrics, 2011. (CentER Discussion Paper).
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abstract = "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 minimises the distance between a vector of weighted integrals of the tail dependence function and their empirical counterparts. The minimisation 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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Einmahl, JHJ, Krajina, A & Segers, J 2011 'An M-Estimator for Tail Dependence in Arbitrary Dimensions' CentER Discussion Paper, vol. 2011-013, Econometrics, Tilburg.

An M-Estimator for Tail Dependence in Arbitrary Dimensions. / Einmahl, J.H.J.; Krajina, A.; Segers, J.

Tilburg : Econometrics, 2011. (CentER Discussion Paper; Vol. 2011-013).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - An M-Estimator for Tail Dependence in Arbitrary Dimensions

AU - Einmahl, J.H.J.

AU - Krajina, A.

AU - Segers, J.

N1 - Subsequently published in Annals of Statistics (2012)

PY - 2011

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N2 - 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 minimises the distance between a vector of weighted integrals of the tail dependence function and their empirical counterparts. The minimisation 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.

AB - 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 minimises the distance between a vector of weighted integrals of the tail dependence function and their empirical counterparts. The minimisation 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.

KW - asymptotic statistics

KW - factor model

KW - M-estimation

KW - multivariate extremes

KW - tail dependence

M3 - Discussion paper

VL - 2011-013

T3 - CentER Discussion Paper

BT - An M-Estimator for Tail Dependence in Arbitrary Dimensions

PB - Econometrics

CY - Tilburg

ER -

Einmahl JHJ, Krajina A, Segers J. An M-Estimator for Tail Dependence in Arbitrary Dimensions. Tilburg: Econometrics. 2011. (CentER Discussion Paper).