Parametric copula adjusted for non- and semiparametric regression

Abstract

We consider a multivariate response regression model where each coordinate is described by a location-scale non-or semi-parametric 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 semi-parametric 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 nonor semi-parametric regression model.

Comparing Some of Robust the Non-Parametric Methods for Semi-Parametric Regression Models Estimation

“…As for the second part of the model, the relationship or function that includes the effect is unknown. This part is estimated by one of the nonparametric methods The Semi-parametric regression model can be represented by the following formula [14].…”