University of Wisconsin Center of Actuarial Excellence
Technology Enhanced Learning Project
Multivariate Regression Using Copulas
It has now been fifty years since the introduction of copulas in 1959 by Sklar in the context of probabilistic metric spaces. Copulas are now a widely used tool in biomedical applications, finance and insurance for understanding relationships among variables whose distribution cannot be approximated by a normal curve.
This presentation introduces copulas and show how they can be used in regression and panel data contexts. I will also give a number of personal examples, mainly from studies risk management and insurance, to illustrate how copulas can be used. Through this introductory material and examples from a specific field, I hope to suggest to viewers how they can use copulas in their own fields of applications.
Presentation - in .pdf format
Lecture - Part A - lecture as a video - Part A. (It is about 65 minutes long)
Lecture - Part B - lecture as a video - Part B. (It is about 40 minutes long)
As a supplement to the presentation, below are tutorials that show how to perform statistical inference (focusing on regression) using copulas. These tutorials are based on the statistical package "R" and use two data sets, also given below.
Description files are in .docx format - Word
Video files are in flash format - they can be viewed on the web.
Rcode files have a .R extension - they are text files.
Illustrative Loss Data - in .csv (comma separated value) format
Illustrative Student Achievement Data - in .csv (comma separated value) format
Date: 6 August 2010