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November 2020 Inference for semiparametric Gaussian copula model adjusted for linear regression using residual ranks
Yue Zhao, Irène Gijbels, Ingrid Van Keilegom
Bernoulli 26(4): 2815-2846 (November 2020). DOI: 10.3150/20-BEJ1208

Abstract

We investigate the inference of the copula parameter in the semiparametric Gaussian copula model when the copula component, subject to the influence of a covariate, is only indirectly observed as the response in a linear regression model. We consider estimators based on residual ranks instead of the usual but unobservable oracle ranks. We first study two such estimators for the copula correlation matrix, one via inversion of Spearman’s rho and the other via normal scores rank correlation estimator. We show that these estimators are asymptotically equivalent to their counterparts based on the oracle ranks. Then, for the copula correlation matrix under constrained parametrizations, we show that the classical one-step estimator in conjunction with the residual ranks remains semiparametrically efficient for estimating the copula parameter. The accuracy of the estimators based on residual ranks is confirmed by simulation studies.

Citation

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Yue Zhao. Irène Gijbels. Ingrid Van Keilegom. "Inference for semiparametric Gaussian copula model adjusted for linear regression using residual ranks." Bernoulli 26 (4) 2815 - 2846, November 2020. https://doi.org/10.3150/20-BEJ1208

Information

Received: 1 April 2019; Revised: 1 February 2020; Published: November 2020
First available in Project Euclid: 27 August 2020

zbMATH: 07256161
MathSciNet: MR4140530
Digital Object Identifier: 10.3150/20-BEJ1208

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

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Vol.26 • No. 4 • November 2020
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