What assumptions must be fulfilled in quantile regression?
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8$\begingroup$ I would say it depends on what inference you want to do with it. My understanding is that it is basically an estimation technique rather than a type of model. So there are no necessary assumption as such unless you are inferring to a data generating process or population. Similarly, OLS has no "assumptions" as such. Although the type of inference it is often associated with assumes constant variance, normality, etc., there is nothing stopping you using OLS without those assumptions applying - it's just a technique for fitting a line. Does this not apply to quantile regression too? $\endgroup$– Peter EllisCommented Jan 17, 2013 at 9:43
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$\begingroup$ The comment by @Peter strikes me as particularly extreme (although not necessarily wrong). Well-established textbooks list basic assumptions of OLS and they all seem to agree on what a core set of them are. It's definitely far more than "just a technique for fitting a line." $\endgroup$– whuber ♦Commented Dec 14, 2016 at 16:13
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1$\begingroup$ Yes, in retrospect my comment is a bit pedantic. The question just needs "as commonly used for inference" implied at the end to be fully answerable; same for OLS. $\endgroup$– Peter EllisCommented Dec 16, 2016 at 21:06
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The advantage of QR techniques is that they do not require, for instance, homoskedasticity of the error terms, strong assumption on the distribution of the covariates. If you are interested in applications to Ecology there is a nice and concise introduction by Cade.
Or if you come from economics, the gentle treatment given by Agrist and Prischke may fit you better.
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7$\begingroup$ What regression techniques require strong assumptions about the distribution of the covariates? $\endgroup$– MacroCommented Jan 17, 2013 at 14:01
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7$\begingroup$ Is the list of assumptions too long to include in an answer? Giving references is useful, but I thought it could be nice to just have the full list included. (Of course, if I read the references and understand what is going on there, I could post an answer myself instead of asking for it from you. But I have never put my hands on quantile regression before so I would not feel too comfortable doing the task.) $\endgroup$ Commented Nov 16, 2015 at 20:22
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$\begingroup$ See post: stats.stackexchange.com/questions/320991/… $\endgroup$ Commented Jan 10, 2019 at 17:38