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

S.U. Can, J.H.J. Einmahl, E.V. Khmaladze, R.J.A. Laeven

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Let (X1, Y1),…., (Xn, Yn) 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
√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 languageEnglish
Place of PublicationTilburg
Number of pages28
Publication statusPublished - 30 Jun 2014

Publication series

NameCentER Discussion Paper


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


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