This Title All WIREs
How to cite this WIREs title:
WIREs Comp Stat

Copulae: An overview and recent developments

Full article on Wiley Online Library:   HTML PDF

Can't access this content? Tell your librarian.

Abstract Over the decades that have passed since they were introduced, copulae still remain a very powerful tool for modeling and estimating multivariate distributions. This work gives an overview of copula theory and it also summarizes the latest results. This article recalls the basic definition, the most important cases of bivariate copulae, and it then proceeds to a sketch of how multivariate copulae are developed both from bivariate copulae and from scratch. Regarding higher dimensions, the focus is on hierarchical Archimedean, vine, and factor copulae, which are the most often used and most flexible ways to introduce copulae to multivariate distributions. We also provide an overview of how copulae can be used in various fields of data science, including recent results. These fields include but are not limited to time series and machine learning. Finally, we describe estimation and testing methods for copulae in general, their application to the presented copula structures, and we give some specific testing and estimation procedures for those specific copulae. This article is categorized under: Statistical Models > Multivariate Models Statistical Models > Semiparametric Models Statistical and Graphical Methods of Data Analysis > Multivariate Analysis
Contour plots of different copulae with Gaussian and t‐distributed margins
[ Normal View | Magnified View ]
The structure of a fully nested hierarchical Gumbel copula with parameters 2, 2.5, and 3 on the left side and the partially nested hierarchical Gumbel copula with parameters 2, 2.5, and 3 on the right side
[ Normal View | Magnified View ]

Browse by Topic

Statistical and Graphical Methods of Data Analysis > Multivariate Analysis
Statistical Models > Semiparametric Models
Statistical Models > Multivariate Models

Access to this WIREs title is by subscription only.

Recommend to Your
Librarian Now!

The latest WIREs articles in your inbox

Sign Up for Article Alerts