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October 2014 Semiparametric Gaussian copula models: Geometry and efficient rank-based estimation
Johan Segers, Ramon van den Akker, Bas J. M. Werker
Ann. Statist. 42(5): 1911-1940 (October 2014). DOI: 10.1214/14-AOS1244

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.

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Johan Segers. Ramon van den Akker. Bas J. M. Werker. "Semiparametric Gaussian copula models: Geometry and efficient rank-based estimation." Ann. Statist. 42 (5) 1911 - 1940, October 2014. https://doi.org/10.1214/14-AOS1244

Information

Published: October 2014
First available in Project Euclid: 11 September 2014

zbMATH: 1305.62115
MathSciNet: MR3262472
Digital Object Identifier: 10.1214/14-AOS1244

Subjects:
Primary: 62F12 , 62G20
Secondary: 62B15 , 62H20

Keywords: Adaptivity , Correlation matrix , influence function , quadratic form , ranks , score function , tangent space

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 5 • October 2014
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