Volume 5, 2022
Statistical Inference in Markov Processes and Copula Models
|Number of page(s)||9|
|Section||Mathematics - Applied Mathematics|
|Published online||21 December 2022|
Conditional independence and predictive copula
Department of Statistics, University of Campinas, Sergio Buarque de Holanda, 651, Campinas, S.P. CEP: 13083-859, Brazil
2 University of Campinas, Sergio Buarque de Holanda, 651, Campinas, S.P. CEP: 13083-859, Brazil
* Corresponding author: email@example.com
Accepted: 10 November 2022
In this paper, we address the concept of conditional independence between two random variables X and Y given the entity Θ. 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 Θ and between Y and Θ. 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 Θ.
Key words: Dependence / Exchangeability / Representations of de Finetti
© V.A. González-López & V. Litvinoff Justus, Published by EDP Sciences, 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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