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 |
|---|---|
| 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 |
|---|---|
| Volume | 2014-041 |
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Keywords
- Extreme value theory
- tail dependence
- goodness-of-fit testing
- martingale transformation
Cite this
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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.
Tilburg : Econometrics, 2014. (CentER Discussion Paper; Vol. 2014-041).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 -