PreprintCC BY 4.0arXiv
How far are d-dimensional copulas with uniform (d−1)-marginals from (total) independence?
Abstract
We consider the family 𝒞dΠd−1 of all d-dimensional copulas whose (d−1)-dimensional marginals are all equal to the (d−1)-dimensional product copula Πd−1 and tackle the natural question, `how far away' from the d-dimensional product copula Πd elements in 𝒞dΠd−1 can be. We provide definitive answers for both, the uniform metric d∞ as well as the stronger, conditioning-based metric D1. The established results clearly indicate that the family 𝒞dΠd−1 is larger than one might expect.
Versions
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BibTeX
@misc{bukovsek2026ddimensional,
title = {{How far are $d$-dimensional copulas with uniform $(d-1)$-marginals from (total) independence?}},
author = {Damjana Kokol Bukovšek and Nik Stopar and Wolfgang Trutschnig},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.18286},
eprint = {2608.18286},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.18286},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - How far are d-dimensional copulas with uniform (d−1)-marginals from (total) independence?
AU - Damjana Kokol Bukovšek
AU - Nik Stopar
AU - Wolfgang Trutschnig
PY - 2026
DA - 2026/08/18
PB - arXiv
DO - 10.48550/arxiv.2608.18286
UR - https://arxiv.org/abs/2608.18286
AB - We consider the family 𝒞_d^Π_d−1 of all d-dimensional copulas whose (d−1)-dimensional marginals are all equal to the (d−1)-dimensional product copula Π_d−1 and tackle the natural question, `how far away' from the d-dimensional product copula Π_d elements in 𝒞_d^Π_d−1 can be. We provide definitive answers for both, the uniform metric d_∞ as well as the stronger, conditioning-based metric D_1. The established results clearly indicate that the family 𝒞_d^Π_d−1 is larger than one might expect.
ER -