### Abstract

Original language | English |
---|---|

Place of Publication | Tilburg |

Publisher | Econometrics |

Number of pages | 16 |

Volume | 2009-42 |

Publication status | Published - 2009 |

### Publication series

Name | CentER Discussion Paper |
---|---|

Volume | 2009-42 |

### Fingerprint

### Keywords

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

### Cite this

*A Method of Moments Estimator of Tail Dependence in Elliptical Copula Models*. (CentER Discussion Paper; Vol. 2009-42). Tilburg: Econometrics.

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

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

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

AU - Krajina, A.

N1 - Pagination: 16

PY - 2009

Y1 - 2009

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

ER -