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April 2015 Asymptotically distribution-free goodness-of-fit testing for tail copulas
Sami Umut Can, John H. J. Einmahl, Estate V. Khmaladze, Roger J. A. Laeven
Ann. Statist. 43(2): 878-902 (April 2015). DOI: 10.1214/14-AOS1304


Let $(X_{1},Y_{1}),\ldots,(X_{n},Y_{n})$ be an i.i.d. sample from a bivariate distribution function that lies in the max-domain of attraction of an extreme value distribution. The asymptotic joint distribution of the standardized component-wise maxima $\bigvee_{i=1}^{n}X_{i}$ and $\bigvee_{i=1}^{n}Y_{i}$ 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.


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Sami Umut Can. John H. J. Einmahl. Estate V. Khmaladze. Roger J. A. Laeven. "Asymptotically distribution-free goodness-of-fit testing for tail copulas." Ann. Statist. 43 (2) 878 - 902, April 2015.


Published: April 2015
First available in Project Euclid: 23 March 2015

zbMATH: 1312.62072
MathSciNet: MR3325713
Digital Object Identifier: 10.1214/14-AOS1304

Primary: 62G10 , 62G20 , 62G32
Secondary: 62F03

Keywords: Extreme value theory , goodness-of-fit testing , martingale transform , tail dependence

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.43 • No. 2 • April 2015
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