## Copula Based Non-linear Regression

Occasional Contributor
Posts: 13

# Copula Based Non-linear Regression

Hi everyone and Happy Friday,

I'm working with data that does not have a normal distribution nor do response/explanatory variables have a linear relationship. I came across the concept of CQR (copula quantile regression) that doesn't seem to require the assumptions that regular linear regression require. Is there a way to do CQR in SAS? I know there's proc quantreg but I thought that only works for a linear quantile regression. Suggestions?

Thanks!

Super User
Posts: 10,787

## Re: Copula Based Non-linear Regression

Not sure.

You could try PROC LASS which can do nonparameter regression .No need Data Distribution,No need Link Function.

Xia Keshan

Posts: 2,655

## Re: Copula Based Non-linear Regression

Hey xia--did you mean PROC LOESS?

Also, if the original poster has SAS/ETS installed, then PROC COPULA may be of interest.  Quantile estimates are obtained by multi-stage analyses, as outlined in Example 10.1 Copula Based VaR Estimation, which gives quantile estimates via PROC UNIVARIATE after a fair amount of pre-processing using PROC COPULA.

Steve Denham

Super User
Posts: 10,787

## Re: Copula Based Non-linear Regression

Yeah, Steve it is LOESS. I got confused .

SAS Super FREQ
Posts: 4,245

## Re: Copula Based Non-linear Regression

Steve,

You make an interesting observation. I didn't think that PROC COPULA could handle regression-type problems (which have a response variable).  The FIT statement fits the parameters of a copula to model the joint distribution function of the variables, and I never considered looking at conditional means or quantiles of the response, given the other variables.

I found an interesting paper http://www.variancejournal.org/issues/05-01/45.pdf (Parsa and Klugman, 2011) in which the authors mention that they use SAS/IML for the optimization and for some numerical integration that must be performed for the generalized linear model regression example.

The authors provide some simulated data and examples.The motivated SAS/IML programmer could probably replicate their examples.