Semiparametric Gaussian copula models: Geometry and efficient rank-based estimation

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20 Citations (Scopus)


We propose, for multivariate Gaussian copula models with unknown margins and structured correlation matrices, a rank-based, semiparametrically efficient estimator for the Euclidean copula parameter. This estimator is defined as a one-step update of a rank-based pilot estimator in the direction of the efficient influence function, which is calculated explicitly. Moreover, finite-dimensional algebraic conditions are given that completely characterize efficiency of the pseudo-likelihood estimator and adaptivity of the model with respect to the unknown marginal distributions. For correlation matrices structured according to a factor model, the pseudo-likelihood estimator turns out to be semiparametrically efficient. On the other hand, for Toeplitz correlation matrices, the asymptotic relative efficiency of the pseudo-likelihood estimator can be as low as 20%. These findings are confirmed by Monte Carlo simulations. We indicate how our results can be extended to joint regression models.
Original languageEnglish
Pages (from-to)1911-1940
JournalAnnals of Statistics
Issue number5
Publication statusPublished - 2014


  • Adaptivity
  • correlation matrix
  • influence function
  • quadratic form
  • ranks
  • score function
  • tangent space


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