A Method of Moments Estimator of Tail Dependence in Elliptical Copula Models

A. Krajina

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Abstract

An elliptical copula model is a distribution function whose copula is that of an elliptical distri- bution. The tail dependence function in such a bivariate model has a parametric representation with two parameters: a tail parameter and a correlation parameter. The correlation parameter can be estimated by robust methods based on the whole sample. Using the estimated correla- tion parameter as plug-in estimator, we then estimate the tail parameter applying a modification of the method of moments approach proposed in the paper by J.H.J. Einmahl, A. Krajina and J. Segers [Bernoulli 14(4), 2008, 1003-1026]. We show that such an estimator is consistent and asymptotically normal. Also, we derive the joint limit distribution of the estimators of the two parameters. By a simulation study, we illustrate the small sample behavior of the estimator of the tail parameter and we compare its performance to that of the estimator proposed in the paper by C. KlÄuppelberg, G. Kuhn and L. Peng [Scandinavian Journal of Statistics 35(4), 2008, 701-718].
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages16
Volume2009-42
Publication statusPublished - 2009

Publication series

NameCentER Discussion Paper
Volume2009-42

Fingerprint

Tail Dependence
Copula Models
Moment Estimator
Method of Moments
Estimator
Tail
Two Parameters
Plug-in Estimator
Dependence Function
Elliptical Distribution
Parametric Representation
Limit Distribution
Robust Methods
Copula
Bernoulli
Joint Distribution
Small Sample
Distribution Function
Simulation Study
Statistics

Keywords

  • asymptotic normality
  • elliptical copula
  • elliptical distribution
  • meta-elliptical model
  • method of moments
  • semi-parametric model
  • tail dependence

Cite this

Krajina, A. (2009). A Method of Moments Estimator of Tail Dependence in Elliptical Copula Models. (CentER Discussion Paper; Vol. 2009-42). Tilburg: Econometrics.
Krajina, A. / A Method of Moments Estimator of Tail Dependence in Elliptical Copula Models. Tilburg : Econometrics, 2009. (CentER Discussion Paper).
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abstract = "An elliptical copula model is a distribution function whose copula is that of an elliptical distri- bution. The tail dependence function in such a bivariate model has a parametric representation with two parameters: a tail parameter and a correlation parameter. The correlation parameter can be estimated by robust methods based on the whole sample. Using the estimated correla- tion parameter as plug-in estimator, we then estimate the tail parameter applying a modification of the method of moments approach proposed in the paper by J.H.J. Einmahl, A. Krajina and J. Segers [Bernoulli 14(4), 2008, 1003-1026]. We show that such an estimator is consistent and asymptotically normal. Also, we derive the joint limit distribution of the estimators of the two parameters. By a simulation study, we illustrate the small sample behavior of the estimator of the tail parameter and we compare its performance to that of the estimator proposed in the paper by C. Kl{\"A}uppelberg, G. Kuhn and L. Peng [Scandinavian Journal of Statistics 35(4), 2008, 701-718].",
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Krajina, A 2009 'A Method of Moments Estimator of Tail Dependence in Elliptical Copula Models' CentER Discussion Paper, vol. 2009-42, Econometrics, Tilburg.

A Method of Moments Estimator of Tail Dependence in Elliptical Copula Models. / Krajina, A.

Tilburg : Econometrics, 2009. (CentER Discussion Paper; Vol. 2009-42).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - A Method of Moments Estimator of Tail Dependence in Elliptical Copula Models

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N1 - Pagination: 16

PY - 2009

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N2 - An elliptical copula model is a distribution function whose copula is that of an elliptical distri- bution. The tail dependence function in such a bivariate model has a parametric representation with two parameters: a tail parameter and a correlation parameter. The correlation parameter can be estimated by robust methods based on the whole sample. Using the estimated correla- tion parameter as plug-in estimator, we then estimate the tail parameter applying a modification of the method of moments approach proposed in the paper by J.H.J. Einmahl, A. Krajina and J. Segers [Bernoulli 14(4), 2008, 1003-1026]. We show that such an estimator is consistent and asymptotically normal. Also, we derive the joint limit distribution of the estimators of the two parameters. By a simulation study, we illustrate the small sample behavior of the estimator of the tail parameter and we compare its performance to that of the estimator proposed in the paper by C. KlÄuppelberg, G. Kuhn and L. Peng [Scandinavian Journal of Statistics 35(4), 2008, 701-718].

AB - An elliptical copula model is a distribution function whose copula is that of an elliptical distri- bution. The tail dependence function in such a bivariate model has a parametric representation with two parameters: a tail parameter and a correlation parameter. The correlation parameter can be estimated by robust methods based on the whole sample. Using the estimated correla- tion parameter as plug-in estimator, we then estimate the tail parameter applying a modification of the method of moments approach proposed in the paper by J.H.J. Einmahl, A. Krajina and J. Segers [Bernoulli 14(4), 2008, 1003-1026]. We show that such an estimator is consistent and asymptotically normal. Also, we derive the joint limit distribution of the estimators of the two parameters. By a simulation study, we illustrate the small sample behavior of the estimator of the tail parameter and we compare its performance to that of the estimator proposed in the paper by C. KlÄuppelberg, G. Kuhn and L. Peng [Scandinavian Journal of Statistics 35(4), 2008, 701-718].

KW - asymptotic normality

KW - elliptical copula

KW - elliptical distribution

KW - meta-elliptical model

KW - method of moments

KW - semi-parametric model

KW - tail dependence

M3 - Discussion paper

VL - 2009-42

T3 - CentER Discussion Paper

BT - A Method of Moments Estimator of Tail Dependence in Elliptical Copula Models

PB - Econometrics

CY - Tilburg

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Krajina A. A Method of Moments Estimator of Tail Dependence in Elliptical Copula Models. Tilburg: Econometrics. 2009. (CentER Discussion Paper).