Measures of Non-simplifyingness for Conditional Copulas and Vines

Alexis Derumigny ()
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Alexis Derumigny: Delft University of Technology, Department of Applied Mathematics

A chapter in Statistical Dependence Modeling, 2026, pp 131-152 from Springer

Abstract: Abstract In copula modeling, the simplifying assumption has recently been the object of much interest. Although it is very useful to reduce the computational burden, it remains far from obvious whether it is actually satisfied in practice. We propose a theoretical framework which aims at giving a precise meaning to the following question: how non-simplified or close to be simplified is a given conditional copula? For this, we propose a new framework centered at the notion of measure of non-constantness. Then we discuss generalizations of the simplifying assumption to the case where the conditional marginal distributions may not be continuous, and corresponding measures of non-simplifyingness in this case. The simplifying assumption is of particular importance for vine copula models, and we therefore propose a notion of measure of non-simplifyingness of a given copula for a particular vine structure, as well as different scores measuring how non-simplified such vine decompositions would be for a general vine. Finally, we propose estimators for these measures of non-simplifyingness given an observed dataset. A small simulation study shows the performance of a few estimators of these measures of non-simplifyingness.

Keywords: Measure of non-constantness; Non-constant functions; Vine copula models; Simplifying assumption; Non-simplified copulas; Non-simplified vines; 62H05 (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-14252-8_7

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DOI: 10.1007/978-3-032-14252-8_7

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