Semiparametric Gaussian copula models: Geometry and efficient rank-based estimation
Segers,J. van den Akker,R. Werker,B.J.M.
Segers,J.
van den Akker,R.
Werker,B.J.M.
Abstract
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.
Description
Date
2014
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Volume Title
Publisher
Research Projects
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Keywords
Adaptivity, correlation matrix, influence function, quadratic form, ranks, score function, tangent space
Citation
Segers, J, van den Akker, R & Werker, B J M 2014, 'Semiparametric Gaussian copula models : Geometry and efficient rank-based estimation', Annals of Statistics, vol. 42, no. 5, pp. 1911-1940. https://doi.org/10.1214/14-AOS1244