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

S.U. Can, John Einmahl, R.J.A. Laeven

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Abstract

Consider a random sample from a continuous multivariate distribution function
F with copula C. In order to test the null hypothesis that C belongs to a certain
parametric family, we construct an under H0 asymptotically distribution-free process that serves as a tests generator. The process is a transformation of the difference of a semi-parametric and a parametric estimator of C. This transformed empirical process converges weakly to a standard multivariate Wiener process, paving the way for a multitude of powerful asymptotically distribution-free goodness-of-t tests for copula families. We investigate the finite-sample performance of our approach through a simulation study and illustrate its applicability with a data analysis.
Original languageEnglish
Place of PublicationTilburg
PublisherCentER, Center for Economic Research
Number of pages33
Volume2017-052
Publication statusPublished - 11 Dec 2017

Publication series

NameCentER Discussion Paper
Volume2017-052

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Keywords

  • Khmaladze transform,
  • copula estimation
  • empirical process

Cite this

Can, S. U., Einmahl, J., & Laeven, R. J. A. (2017). Asymptotically Distribution-Free Goodness-of-Fit Testing for Copulas. (CentER Discussion Paper; Vol. 2017-052). Tilburg: CentER, Center for Economic Research.