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What assumptions must be fulfilled in quantile regression?

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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? – Peter Ellis Jan 17 at 9:43

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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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What regression techniques require strong assumptions about the distribution of the covariates? – Macro Jan 17 at 14:01

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