07-24-2015 04:55 PM
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?
07-27-2015 08:39 AM
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.
07-28-2015 01:55 PM
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.
07-28-2015 01:59 PM
I think the key to using PROC COPULA is to get away from thinking of independent and dependent variables--just a joint distribution. Once you take that step, what is given in the VaR estimation example is pretty straightforward (at least compared to time-dependent copulas that the financial guys are modeling these days).