### Abstract

an extreme value distribution. The asymptotic joint distribution of the standardized component-wise maxima

√n i=1 Xi and √n i=1 Yi is then characterized by the marginal extreme value indices and the tail copula R. We propose a procedure for constructing asymptotically distribution-free goodness-of-fit tests for the tail copula R. The procedure is based on a transformation of a suitable empirical process derived from a semi-parametric estimator of R. The transformed empirical

process converges weakly to a standard Wiener process, paving the way for a multitude of asymptotically distribution-free goodness-of-fit tests. We also extend our results to the m-variate (m > 2) case. In a simulation study we show that the limit theorems provide good approximations for finite samples and that tests based on the transformed empirical process have high power.

Original language | English |
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Place of Publication | Tilburg |

Publisher | Econometrics |

Number of pages | 28 |

Volume | 2014-041 |

Publication status | Published - 30 Jun 2014 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2014-041 |

### Fingerprint

### Keywords

- Extreme value theory
- tail dependence
- goodness-of-fit testing
- martingale transformation

### Cite this

*Asymptotically Distribution-Free Goodness-of-Fit Testing for Tail Copulas*. (CentER Discussion Paper; Vol. 2014-041). Tilburg: Econometrics.

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**Asymptotically Distribution-Free Goodness-of-Fit Testing for Tail Copulas.** / Can, S.U.; Einmahl, J.H.J.; Khmaladze, E.V.; Laeven, R.J.A.

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

TY - UNPB

T1 - Asymptotically Distribution-Free Goodness-of-Fit Testing for Tail Copulas

AU - Can, S.U.

AU - Einmahl, J.H.J.

AU - Khmaladze, E.V.

AU - Laeven, R.J.A.

PY - 2014/6/30

Y1 - 2014/6/30

N2 - Let (X1, Y1),…., (Xn, Yn) be an i.i.d. sample from a bivariate distribution function that lies in the max-domain of attraction ofan extreme value distribution. The asymptotic joint distribution of the standardized component-wise maxima√n i=1 Xi and √n i=1 Yi is then characterized by the marginal extreme value indices and the tail copula R. We propose a procedure for constructing asymptotically distribution-free goodness-of-fit tests for the tail copula R. The procedure is based on a transformation of a suitable empirical process derived from a semi-parametric estimator of R. The transformed empiricalprocess converges weakly to a standard Wiener process, paving the way for a multitude of asymptotically distribution-free goodness-of-fit tests. We also extend our results to the m-variate (m > 2) case. In a simulation study we show that the limit theorems provide good approximations for finite samples and that tests based on the transformed empirical process have high power.

AB - Let (X1, Y1),…., (Xn, Yn) be an i.i.d. sample from a bivariate distribution function that lies in the max-domain of attraction ofan extreme value distribution. The asymptotic joint distribution of the standardized component-wise maxima√n i=1 Xi and √n i=1 Yi is then characterized by the marginal extreme value indices and the tail copula R. We propose a procedure for constructing asymptotically distribution-free goodness-of-fit tests for the tail copula R. The procedure is based on a transformation of a suitable empirical process derived from a semi-parametric estimator of R. The transformed empiricalprocess converges weakly to a standard Wiener process, paving the way for a multitude of asymptotically distribution-free goodness-of-fit tests. We also extend our results to the m-variate (m > 2) case. In a simulation study we show that the limit theorems provide good approximations for finite samples and that tests based on the transformed empirical process have high power.

KW - Extreme value theory

KW - tail dependence

KW - goodness-of-fit testing

KW - martingale transformation

M3 - Discussion paper

VL - 2014-041

T3 - CentER Discussion Paper

BT - Asymptotically Distribution-Free Goodness-of-Fit Testing for Tail Copulas

PB - Econometrics

CY - Tilburg

ER -