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Copula Based Regression

Recently I ran across an article in the Casualty
Actuarial Society's publication Variance that discussed copula based
regression.
From the abstract:
*In this paper, we present copula regression as an
alternative to OLS and GLM. The major advantage of a copula
regression is that there are no restrictions on the probability
distributions that can be used. In this paper, we will present the
formulas and algorithms necessary for conducting a copula regression
analysis using the normal copula. However, the ideas presented here
can be used with any copula function that can incorporate multiple
variables with varying degrees of association.*

In the paper
they outline a 3 step process for accomplishing this:

*1)
Assume a model for the joint distribution of all the variables
(response and covariates)*
*2) Estimate the parameters of the model (the
parameters for the selected marginal distributions and the parameters
of the copula)*
*3) Compute the predicted values of Y given a set
of covariates by using the conditional mean of Y given the
covariates.*

I'd also like to point out this interesting virtual
course on copula regression from Dr. Edward Frees at the University
of Wisconsin:
https://sites.google.com/a/wisc.edu/jed-frees/multivariate-regression-using-copulas
I have not had a chance to view these materials in
detail, but absolutely think it could be valuable to anyone wanting
to learn more about these methods.
**Additional Reading:**
Modeling Dependence with Copulas and R
Copula Based Agricultural Risk Models
Intro to Copulas using SAS
Copulas, R, and the Financial Crisis
**References: **
Parsa, Rahul A, and Stuart A. Klugman, "Copula
Regression," *Variance* 5:1, 2011, pp. 45-54.
Link:
http://www.variancejournal.org/issues/?fa=article&abstrID=6831
Link:
http://www.variancejournal.org/issues/05-01/45.pdf
Presentation:
http://www.casact.org/research/dare/documents/P1-Parsa_1.pdf

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