Crossing quantile regression lines

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YJD
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Crossing quantile regression lines

I used proc quantreg to fit 95 and 99 quantile regression lines, and found that the two fitted lines intersect.  Is there any SAS procedure, macro, or method that can provide a "Simultaneous multiple non-crossing quantile regression"?

Thanks in advance.

SAS Super FREQ
Posts: 3,752

Re: Crossing quantile regression lines

This is called "the quantile crossing problem." In my experience, it happens more often with extreme quantiles. In a recent publication, Bondell, Reich, and Wang (2010) state "this problem is well known, but no simple and general solution currently exists."  http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3371721/

The authors show how to formulate the quantile regression problem in terms of a big linear programming problem. I do not think PROC QUANTREG provides an option to avoid the quantile crossing problem.  In SAS, you would probably solve this problem by using the linear programming (LP) solver in the OPTMODEL procedure in SAS/OR software.

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