Abstract
We consider a multivariate response regression model where each coordinate is described by a location-scale non- or semiparametric regression and where the dependence structure of the “noise term” is described by a parametric copula. Our goal is to estimate the associated Euclidean copula parameter, given a sample of the response and the covariate. In the absence of the copula sample, the usual oracle ranks are no longer computable. Instead, we study the normal scores estimator for the Gaussian copula and generalized pseudo-likelihood estimation for general parametric copulas, both based on residual ranks calculated from preliminary non- or semiparametric estimators of the location and scale functions. We show that the residual-based estimators are asymptotically equivalent to their oracle counterparts and provide explicit rate of convergence. Partially to serve this objective, we also study weighted convergence of the residual empirical process under the non- or semiparametric regression model.
Funding Statement
Research was supported by the European Research Council (2016-2021, Horizon 2020 / ERC grant agreement No. 694409), and by C1-project C16/20/002 from the Research Council KU Leuven.
Acknowledgements
We thank a Co-Editor, an Associate Editor, and three anonymous referees for their insightful comments and for encouraging us to carry out the study in Section 5.
Citation
Yue Zhao. Irène Gijbels. Ingrid Van Keilegom. "Parametric copula adjusted for non- and semiparametric regression." Ann. Statist. 50 (2) 754 - 780, April 2022. https://doi.org/10.1214/21-AOS2126
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