Semiparametric Gaussian Copula Models: Geometry and Efficient Rank-Based Estimation

47 Pages Posted: 12 Aug 2013

See all articles by Johan Segers

Johan Segers

Catholic University of Louvain (UCL)

Ramon Van den Akker

Tilburg University - CentER and department of Econometrics & OR

Bas J. M. Werker

Tilburg University - Center for Economic Research (CentER)

Date Written: June 28, 2013

Abstract

For multivariate Gaussian copula models with unknown margins and structured correlation matrices, a rank-based, semiparametrically efficient estimator is proposed 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 adaptivity of the model with respect to the unknown marginal distributions and of efficiency of the pseudo-likelihood estimator. 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 with respect to our one-step estimator can be as low as 20%. These findings are confirmed by Monte Carlo simulations.

Keywords: adaptivity, correlation matrix, influence function, quadratic form, ranks, score function, tangent space

JEL Classification: C14

Suggested Citation

Segers, Johan and Van den Akker, Ramon and Werker, Bas J.M., Semiparametric Gaussian Copula Models: Geometry and Efficient Rank-Based Estimation (June 28, 2013). Available at SSRN: https://ssrn.com/abstract=2308596 or http://dx.doi.org/10.2139/ssrn.2308596

Johan Segers (Contact Author)

Catholic University of Louvain (UCL) ( email )

Place Montesquieu, 3
Louvain-la-Neuve, 1348
Belgium
+32 10 474311 (Phone)
+32 10 473032 (Fax)

HOME PAGE: http://www.uclouvain.be/stat

Ramon Van den Akker

Tilburg University - CentER and department of Econometrics & OR ( email )

K-623
PO Box 90153
Tilburg, 5000 LE
Netherlands

HOME PAGE: http://sites.google.com/site/rvdnakker/

Bas J.M. Werker

Tilburg University - Center for Economic Research (CentER) ( email )

Econometrics and Finance Group
5000 LE Tilburg
Netherlands

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