While trying to perform some quantile regressions on some data I have encountered a classic problem: the 0.25,0.50, 0.75, 0.95 quantile curves are crossing each other (I am dealing with linear curves).
I am currently working with Stata using the sqreg command.
I have read Howard Bondell's paper "Non-crossing quantile regression curve estimation"(2010) and I know he used R to code a solution.
I have also read papers from Andriyana and from Chernozhukov (on the issue of non-monotonicity issues in quantile regressions).
Just to be clear about what we are talking, here below is an example of quantile curves that DO NOT CROSS (and my issue is what to do when they cross):
I was wondering if any of you could recommend what software solutions are most commonly used in the working practice, to deal with crossing quantile curves (=to avoid their crossing), I know there are various methods, so the question is both: what method you prefer and what software would you to use to solve the issue?
Note: I am not posting a sample of my data because it's irrelevant, I am just interested in the general theory of the problem and how to deal with it specifically with software (ideally STATA or Mathematica, or R or Python or Perl).