Goodness-of-fit testing for copulas: A distribution-free approach

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 empirical process on the unit hypercube that converges weakly to a standard Wiener process under the null hypothesis. This process can therefore serve as a ‘tests generator’ for asymptotically distribution-free goodness-of-fit testing of copula families. We also prove maximal sensitivity of this process to contiguous alternatives. Finally, we demonstrate through a
Monte Carlo simulation study that our approach has excellent finite-sample performance, and we illustrate its applicability with a data analysis.
Original languageEnglish
Pages (from-to)3163-3190
JournalBernoulli
Volume26
Issue number4
DOIs
Publication statusPublished - Aug 2020

Keywords

  • Copula
  • goodness-of-fit
  • distribution-free
  • semi-parametric estimation
  • Monte Carlo simulation

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