Bivariate quadratic copula constructions

In this work, we prove that quadratic transformations of aggregation functions must come from quadratic aggregation functions. We also show that this is different from quadratic transformations of (multivariate) semi-copulas and quasi-copulas. In the latter case, those two classes are actually the same and consists of convex combinations of the identity map and another fixed quadratic transformation. In other words, it is a convex set with two extreme points. This result is different from the bivariate case in which the two classes are different and both are convex with four extreme points.

show abstract

“…Several works has been done for k = , see [4,7,8,11,12]. For quadratic polynomial P, the following result is known.…”

Section: Basic Concepts and Terminologiesmentioning

confidence: 99%

“…We are interested in the method of transformations, that is, a method that transforms aggregation functions into other aggregation functions. Such methods have been studied by several others [4,7,8,11,12]. However, most of these studies are only applied to bivariate aggregation functions.…”

Section: Introductionmentioning

confidence: 99%

Quadratic transformation of multivariate aggregation functions

Boonmee

Tasena

2020

Dependence Modeling

Self Cite

View full text Add to dashboard Cite

show abstract

“…Copulas have been widely used for modelling the stochastic dependence among random quantities, mainly in the context of empirical applications (see, e.g., Jondeau and Rockinger, 2006;Zimmer and Trivedi, 2006;Sriboonchitta et al, 2017). This explains the interest for this methodological tool under a theoretical point of view, with a growing interest in constructing new families of copulas and assessing their features (see, e.g., Demarta and McNeil, 2005;Durante et al, 2008;Mesiar et al, 2010;Durante et al, 2017;Wisadwongsa and Tasena, 2018).…”

Section: Introductionmentioning

confidence: 99%

Copulas, uncertainty, and false discovery rate control

Cerqueti

Lupi

2018

International Journal of Approximate Reasoning

View full text Add to dashboard Cite

The false discovery rate (fdr) is a powerful approach to multiple testing. However, dependence among test statistics is critical for fdr control. The way in which this dependence structure is described represents the most prominent source of uncertainty of this statistical theme. copulas play a relevant role among the techniques used to deal with uncertainty and dependence. This paper contributes to fill an existing gap in the scientific debate by exploring the connections between the literature on fdr and that on copulas. In particular, we aim at attracting the interest of the scientific community on this topic by identifying suitable classes of nonstandard copulas which ensure that fdr control can be attained for dependent test statistics.

show abstract