Having a fitted quantile regression (forest) model is great. However, how does one choose the best quantile to perform the actual prediction?

One idea would be to use bootstrapping. In other words, re-sample from the (training?) data and calculate the error distribution (e.g. RMSE) for different quantiles. The distribution of the quantile with the lowest mean/median error (and smallest variance?) could be used to predict.

What do you think? Any other input would be very much appreciated.

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    $\begingroup$ YOU decide which quantile you want to predict, or, more generally, you decide what aspect of the distribution you want to predict. Maybe you express that via a loss function. Only when YOU have decided what you want to predict, statistics can start! Statistical theory cannot tell YOU which question YOU want to ask from the data (and model.) $\endgroup$ – kjetil b halvorsen Mar 5 '19 at 21:05
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    $\begingroup$ See e.g. stats.stackexchange.com/q/160354/17230. You might be interested in predicting a set of quantiles: see the predicted birth weight by maternal weight gain example in Flom, NESUG 2011, "Quantile regression with PROC QUANTREG " $\endgroup$ – Scortchi - Reinstate Monica Mar 6 '19 at 15:01
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    $\begingroup$ a) Thanks @Scortchi for the cite. b) Your proposal makes no sense. Your proposal might tell you which quantile is most precisely estimated, but that just gives you a precise estimate of the wrong thing. If you want to predict the median, a precise estimate of the 90 %tile is not going to help. $\endgroup$ – Peter Flom Mar 7 '19 at 12:57

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