1. Extending multivariate sub-quasi-copulasDamjana Kokol-Bukovšek, Tomaž Košir, Blaž Mojškerc, Matjaž Omladič, 2024, original scientific article 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. Keywords: mathematics, multivariate analysis Published in DiRROS: 18.06.2024; Views: 246; Downloads: 140 Full text (430,71 KB) This document has many files! More... |
2. |
3. Coherence and avoidance of sure loss for standardized functions and semicopulasErich Peter Klement, Damjana Kokol-Bukovšek, Blaž Mojškerc, Matjaž Omladič, Susanne Saminger, Nik Stopar, 2024, original scientific article Abstract: We discuss avoidance of sure loss and coherence results for semicopulas and standardized functions, i.e., for grounded, $1$-increasing functions with value $1$ at $(1, 1, \ldots , 1)$. We characterize the existence of a $k$-increasing $n$-variate function $C$ fulfilling $A \le C \le B$ for standardized $n$-variate functions $A$, $B$ and discuss methods for constructing such functions. Our proofs also include procedures for extending functions on some countably infinite mesh to functions on the unit box. We provide a characterization when $A$ respectively $B$ coincides with the pointwise infimum respectively supremum of the set of all $k$-increasing $n$-variate functions $C$ fulfilling $A \le C \le B$. Keywords: copulas, quasi-copulas, semicopulas, standardized function, coherence, avoidance of sure loss, k-increasing function Published in DiRROS: 13.03.2024; Views: 361; Downloads: 190 Full text (992,65 KB) This document has many files! More... |
4. On the exact region determined by Spearman's rho and Spearman's footruleDamjana Kokol-Bukovšek, Nik Stopar, 2024, original scientific article Abstract: We determine the lower bound for possible values of Spearman’s rho of a bivariate copula given that the value of its Spearman's footrule is known and show that this bound is always attained. We also give an estimate for the exact upper bound and prove that the estimate is exact for some but not all values of Spearman's footrule. Nevertheless, we show that the estimate is quite tight. Keywords: copula, dependence concepts, supremum and infimum of a set of copulas, measures of concordance, quasi-copula, local bounds Published in DiRROS: 13.03.2024; Views: 392; Downloads: 173 Full text (1,55 MB) This document has many files! More... |