Extraction dependence structure of distorted copulas via a measure of dependence

Hien Duy Tran (), Uyen Hoang Pham (), Sel Ly () and T. Vo-Duy ()
Additional contact information
Hien Duy Tran: Tan Tao University
Uyen Hoang Pham: University of Economics and Law
Sel Ly: Ton Duc Thang University
T. Vo-Duy: Ton Duc Thang University

Annals of Operations Research, 2017, vol. 256, issue 2, No 3, 236 pages

Abstract: Abstract Copulas are one of the most powerful tools in modeling dependence structure of multivariate variables. In Tran et al. (Integrated uncertainty in knowledge modelling and decision making. Springer, Berlin, pp 126–137, 2015), we have constructed a new measure of dependence, $$\lambda (C),$$ λ ( C ) , based on Sobolev norm for copula C which can be used to characterize comonotonicity, countermonotonicity and independence of random vectors. This paper aims to use the measure $$ \lambda (C) $$ λ ( C ) to study how dependence structure of a distorted copula after being transformed by a distortion function is changed. Firstly, we propose two methods to estimate the measure $$\lambda (C)$$ λ ( C ) , one for known copula C using conditional copula-based Monte Carlo simulation and the latter for unknown copula dealing with empirical data. Thereafter, PH-transform $$g_{ PH }$$ g P H of extreme value copulas and Wang’s transform $$ g_\gamma $$ g γ of normal and product copula are studied, and we observe their dependence behaviors changing through variability of the measure $$ \lambda (C) $$ λ ( C ) . Our results show that dependence structure of distorted copulas is subject to comonotonicity as increasing the parametric $$ \gamma $$ γ .

Keywords: Copulas; Distortion functions; Monotone dependence; Comonotonicity; Countermonotonicity; Measures of dependence; Sobolev norm (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://link.springer.com/10.1007/s10479-017-2487-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:256:y:2017:i:2:d:10.1007_s10479-017-2487-2

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-017-2487-2

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().