Conditional independence and predictive copula

Abstract

In this paper, we address the concept of conditional independence between two random variables $X$ and $Y$ given the entity $\Theta$. We identify the impact of conditional independence on the analytic form of the predictive 2-copula between $X$ and $Y$. We obtain a representation of the predictive 2-copula between $X$ and $Y$ in terms of functions associated with the copulas between $X$ and $\Theta$ and between $Y$ and $\Theta$. Through the concept of infinite exchangeable sequences we amplify the validity of our results, obtaining the predictive 2-copula between two variables in terms of the copula between only one of these variables and the quantity $\Theta$.