| Issue |
4open
Volume 5, 2022
Statistical Inference in Markov Processes and Copula Models
|
|
|---|---|---|
| Article Number | 20 | |
| Number of page(s) | 9 | |
| Section | Mathematics - Applied Mathematics | |
| DOI | https://doi.org/10.1051/fopen/2022022 | |
| Published online | 21 December 2022 | |
Research Article
Conditional independence and predictive copula
1
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: v245362@dac.unicamp.br
Received:
13
September
2022
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.