Non-parametric approach for copula-based regression estimation

Copula models are growing ubiquitous attention for modeling multivariate data in modern statistics. Indeed, an exciting characteristic of the copula function is that the regression model can also be written in terms of marginal distributions and copula density. In literature, several estimation techniques have been proposed to estimate the margins and density of the copula function to carry out regression equations. This article presents a new fully non-parametric copula-based estimation framework for estimating the regression function, where margins are estimated non-parametrically via pseudo observations computed through harmonic mean (HM) of the ordered statistics, and copula density is estimated using the local-log quadratic quantile transformation (TLL2) kernel estimation technique. We also provide some basic assumptions and statistical properties for this newly proposed estimator. Extensive numerical experiments are performed to illustrate the practical behavior of the proposed estimator. Finally, a real data application is also presented.