Extending multivariate sub-quasi-copulas

TL;DR

This paper develops new methods for constructing multivariate quasi-copulas using patchwork techniques, providing necessary and sufficient conditions for their existence and exploring the limitations of extending bivariate methods.

Contribution

It introduces novel patchwork constructions for multivariate quasi-copulas and characterizes their existence conditions, advancing the understanding of multivariate dependence modeling.

Findings

Established necessary and sufficient conditions for multivariate quasi-copula existence

Identified limitations of extending bivariate constructions to higher dimensions

Provided all possible solutions for the patchwork constructions

Abstract

In this paper, we introduce patchwork constructions for multivariate quasi-copulas. These results appear to be new since the kind of approach has been limited to either copulas or only bivariate quasi-copulas so far. It seems that the multivariate case is much more involved since we are able to prove that some of the known methods of bivariate constructions cannot be extended to higher dimensions. Our main result is to present the necessary and sufficient conditions both on the patch and the values of it for the desired multivariate quasi-copula to exist. We also give all possible solutions.