Improving Upon the Marginal Empirical Distribution Functions when the Copula is Known

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Abstract

At the heart of the copula methodology in statistics is the idea of separating marginal distributions from the dependence structure. However, as shown in this paper, this separation is not to be taken for granted: in the model where the copula is known and the marginal distributions are completely unknown, the empirical distribution functions are semiparametrically efficient if and only if the copula is the independence copula. Incorporating the knowledge of the copula into a nonparametric likelihood yields an estimation procedure which by simulations is shown to outperform the empirical distribution functions, the amount of improvement depending on the copula. Although the known-copula model is arguably artificial, it provides an instructive stepping stone to the more general model of a parametrically specified copula and arbitrary margins.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages25
Volume2008-40
Publication statusPublished - 2008

Publication series

NameCentER Discussion Paper
Volume2008-40

Keywords

  • independence copula
  • nonparametric maximum likelihood estimator
  • score function
  • semiparametric efficiency
  • tangent space

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