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I am new to quantile regression, I have read the original paper from Koenker and Bassett and also other documents.

I was under the impression that quantile regression is only used with linear regression functions, but after reading this I am confused:

https://mathematicaforprediction.wordpress.com/2013/12/23/quantile-regression-robustness/

The author seems to imply that he can calculate quantile regression for any curve.

Is quantile regression also used with other types of functions other than linear?

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Unlike the answer from @Arne Jonas Warnke , I see no need to restrict attention to non-parametric estimators for nonlinear quantile regression.

Simply use whatever form of nonlinear function of the parameter vector $\beta$ , namely $f(\beta)$, you have in place of $X\beta$ in https://en.wikipedia.org/wiki/Quantile_regression#Conditional_quantile_and_quantile_regression . Of course, if $f(\beta)$ is a nonlinear function of the parameter vector $\beta$, the quantile regression problem will not be a Linear Programming problem, but it could still be solved with an appropriate nonlinear optimization solver.

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  • $\begingroup$ Arne Jonas Warnke and Mark L.Stone, both of you helped me clarify my confusion, now I see where I was wrong. Thank you. $\endgroup$ – Statlearner Dec 5 '16 at 17:46
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Yes, of course, there are non-parametric estimator for quantile regression, see for example Horrowitz and Lee (2004).

But I think there may be some confusion about the meaning of the term linear. See this nice answer here at CrossValidated. The models in the blog post are indeed additive and linear.

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