• Corpus ID: 88518684

An essay on copula modelling for discrete random vectors; or how to pour new wine into old bottles

@article{Geenens2019AnEO,
  title={An essay on copula modelling for discrete random vectors; or how to pour new wine into old bottles},
  author={Gery Geenens},
  journal={arXiv: Methodology},
  year={2019}
}
  • G. Geenens
  • Published 25 January 2019
  • Computer Science
  • arXiv: Methodology
Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Sklar's theorem, "the fundamental theorem of copulas", makes a clear distinction between the continuous case and the discrete case, though. In particular, the copula of a discrete random vector is not identifiable, which causes serious inconsistencies. In spite of this, downplaying statements are widespread in the related literature, and copula methods are used for… 

Quantum Implementation of Risk Analysis-relevant Copulas

TLDR
It turns out that such a discretized copula can be expressed using simple constructs present in the quantum computing: binary fraction expansion format, comonotone/independent random variables, controlled gates, and convex combinations, and is therefore suitable for a quantum computer implementation.

The Hellinger Correlation

Abstract In this article, the defining properties of any valid measure of the dependence between two continuous random variables are revisited and complemented with two original ones, shown to imply

References

SHOWING 1-10 OF 66 REFERENCES

On rank correlation measures for non-continuous random variables

Maximal coupling of empirical copulas for discrete vectors

A Primer on Copulas for Count Data

TLDR
The authors show how the possibility of ties that results from atoms in the probability distribution invalidates various familiar relations that lie at the root of copula theory in the continuous case.

Discrete Multivariate Analysis: Theory and Practice

TLDR
Discrete Multivariate Analysis is a comprehensive text and general reference on the analysis of discrete multivariate data, particularly in the form of multidimensional tables, and contains a wealth of material on important topics.

An Introduction to Copulas

These notes provide an introduction to modeling with copulas. Copulas are the mechanism which allows us to isolate the dependency structure in a multivariate distribution. In particular, we can

Inference for copula modeling of discrete data: a cautionary tale and some facts

TLDR
Some of the mathematical, statistical and epistemological issues involved in using copulas to model discrete data are elucidated and the possible use of (nonparametric) copula methods versus the problematic use of parametric copula models are contrasted.

Association and Estimation in Contingency Tables

OUR 1967 Committee on Publications, chaired by David L. Wallace, found that many American Statistical Association members desired more review and survey papers. These have been hard to come by, and

Copula in a multivariate mixed discrete-continuous model

The Hellinger Correlation

Abstract In this article, the defining properties of any valid measure of the dependence between two continuous random variables are revisited and complemented with two original ones, shown to imply
...